Gr 11 Math Ch 5: Quadratic Function

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What is the domain of a quadratic function?

{x : x ∈ ℝ} (correct)

{x : x ∈ ℝ, x ≥ 0}

{x : x ∈ ℝ, x ≠ -p}

{x : x ∈ ℝ, x ≤ 0}

What is the range of a quadratic function when a > 0?

{y : y ≥ q, y ∈ ℝ} (correct)

{y : y ∈ ℝ}

{y : y ≠ q, y ∈ ℝ}

{y : y ≤ q, y ∈ ℝ}

How do you find the y-intercept of a quadratic function?

Set x = p

Set x = 0 (correct)

Set y = 0

Set y = q

What is the turning point of the quadratic function f(x) = a(x + p)^2 + q?

(-p, q) Signup and view all the answers

What is the axis of symmetry of the quadratic function f(x) = a(x + p)^2 + q?

x = -p Signup and view all the answers

How do you shift the graph of a parabola m units to the right?

Replace x with x - m Signup and view all the answers

What is the equation of a parabola that passes through the points (x1, 0) and (x2, 0)?

y = a(x - x1)(x - x2) Signup and view all the answers

What is the equation of a parabola that has a turning point (p, q) and passes through the point (r, s)?

y = a(x - p)^2 + q Signup and view all the answers

What is the effect of $q$ on the graph of $y = ax^2 + q$?

It shifts the graph vertically. Signup and view all the answers

What is the effect of $a$ on the graph of $y = ax^2 + q$ when $a > 0$?

It makes the graph a 'smile' and has a minimum turning point. Signup and view all the answers

What is the effect of $p$ on the graph of $y = a(x + p)^2 + q$?

It shifts the graph horizontally. Signup and view all the answers

What is the axis of symmetry of the graph of $y = a(x + p)^2 + q$?

The line $x = -p$. Signup and view all the answers

What type of graph does $y = ax^2 + q$ represent when $a > 0$?

A 'smile' shape. Signup and view all the answers

What is the y-intercept of the graph of $y = ax^2 + q$?

The point $(0, q)$. Signup and view all the answers

What happens to the graph of $y = ax^2 + q$ when $a$ gets closer to 0?

The graph becomes wider. Signup and view all the answers

What type of graph does $y = a(x + p)^2 + q$ represent when $a < 0$?

A 'frown' shape. Signup and view all the answers

What is the effect of a negative value of q on the graph of y = ax^2 + q?

The graph is shifted vertically downwards. Signup and view all the answers

What happens to the graph of y = a(x + p)^2 + q when the value of p increases?

The graph shifts to the right. Signup and view all the answers

What is the shape of the graph of y = ax^2 + q when a is negative?

A frown. Signup and view all the answers

What is the turning point of the graph of y = a(x + p)^2 + q when a is positive?

A minimum turning point. Signup and view all the answers

What happens to the graph of y = ax^2 + q when the value of a gets closer to 0?

The graph becomes wider. Signup and view all the answers

What is the effect of a positive value of q on the graph of y = ax^2 + q?

The graph is shifted vertically upwards. Signup and view all the answers

What is the turning point of the graph of y = a(x + p)^2 + q when a is negative?

A maximum turning point. Signup and view all the answers

What happens to the graph of y = a(x + p)^2 + q when the value of a gets smaller?

The graph becomes narrower. Signup and view all the answers

What is the effect of shifting the equation of a parabola y = ax^2 + q, q units down?

The graph is shifted q units up Signup and view all the answers

What is the form of the axis of symmetry for the graph of y = a(x + p)^2 + q?

x = -p Signup and view all the answers

What is the turning point of the graph of y = a(x - p)^2 + q?

(p, q) Signup and view all the answers

What information is required to find the equation of a parabola in the form y = a(x - x1)(x - x2)?

Y-intercept and x-intercepts Signup and view all the answers

What is the effect of shifting the equation of a parabola y = ax^2, m units to the left?

Replace x with x - m Signup and view all the answers

What is the form of the equation of a parabola that has a turning point (p, q) and passes through the point (r, s)?

y = a(x - p)^2 + q Signup and view all the answers

What is the y-intercept of the graph of y = ax^2 + q?

(0, q) Signup and view all the answers

What is the effect of shifting the equation of a parabola y = a(x + p)^2 + q, n units up?

Replace y with y + n Signup and view all the answers

What is the effect of increasing the value of $p$ on the graph of $y = a(x + p)^2 + q$?

The graph is shifted horizontally to the left. Signup and view all the answers

What is the shape of the graph of $y = ax^2 + q$ when $a$ is negative?

A parabola with a maximum turning point Signup and view all the answers

What is the effect of decreasing the value of $a$ on the graph of $y = a(x + p)^2 + q$?

The graph is wider and has a minimum turning point. Signup and view all the answers

What is the axis of symmetry of the graph of $y = a(x + p)^2 + q$?

The line $x = -p$ Signup and view all the answers

What is the effect of $q$ on the graph of $y = ax^2 + q$ when $q > 0$?

The graph is shifted vertically upwards. Signup and view all the answers

What is the effect of increasing the value of $a$ on the graph of $y = ax^2 + q$?

The graph is narrower and has a minimum turning point. Signup and view all the answers

What is the turning point of the graph of $y = a(x + p)^2 + q$ when $a > 0$?

A minimum turning point Signup and view all the answers

What is the effect of decreasing the value of $q$ on the graph of $y = ax^2 + q$?

The graph is shifted vertically downwards. Signup and view all the answers

What is the range of the quadratic function f(x) = a(x + p)^2 + q if a < 0?

All real numbers less than or equal to q Signup and view all the answers

If the graph of a quadratic function has a turning point at (-2, 3), what is the corresponding equation of the quadratic function in the form f(x) = a(x + p)^2 + q?

f(x) = a(x + 2)^2 + 3 Signup and view all the answers

What is the effect of shifting the graph of y = ax^2 + q, 2 units to the right?

Replace x with x + 2 Signup and view all the answers

What is the equation of a parabola that has x-intercepts at 2 and 4, and passes through the point (3, 5)?

y = a(x - 2)(x - 4) Signup and view all the answers

If the graph of a quadratic function has a y-intercept at (0, 2), what is the corresponding equation of the quadratic function in the form f(x) = a(x + p)^2 + q?

f(x) = a(x + 0)^2 + 2 Signup and view all the answers

What is the effect of shifting the equation of a parabola y = ax^2, 3 units down?

Replace y with y - 3 Signup and view all the answers

What is the axis of symmetry of the graph of y = a(x + 2)^2 + 3?

x = -2 Signup and view all the answers

What is the equation of a parabola that passes through the points (1, 0) and (3, 0), and has a turning point at (2, 4)?

y = a(x - 1)(x - 3) + 4 Signup and view all the answers

What is the effect of a large value of a on the graph of y = ax^2 + q?

The graph becomes narrower Signup and view all the answers

What is the effect of p on the turning point of the graph of y = a(x + p)^2 + q?

It shifts the turning point to the right Signup and view all the answers

What is the effect of q on the graph of y = ax^2 + q when q is negative?

The graph shifts vertically downwards Signup and view all the answers

What is the shape of the graph of y = ax^2 + q when a is positive?

A 'smile' shape Signup and view all the answers

What is the axis of symmetry of the graph of y = a(x + p)^2 + q?

The line x = -p Signup and view all the answers

What is the effect of a negative value of a on the graph of y = ax^2 + q?

The graph becomes a 'frown' shape Signup and view all the answers

What is the effect of increasing the value of p on the graph of y = a(x + p)^2 + q?

The graph shifts to the right Signup and view all the answers

What is the effect of decreasing the value of a on the graph of y = ax^2 + q?

The graph becomes wider Signup and view all the answers

What is the effect of a negative value of a on the graph of y = a(x + p)^2 + q?

It opens downwards. Signup and view all the answers

What is the equation of a parabola that has a turning point at (-1, 2) and passes through the point (0, 4)?

y = -(x + 1)^2 + 2 Signup and view all the answers

What is the axis of symmetry of the graph of y = a(x - 2)^2 + 3?

x = -2 Signup and view all the answers

What is the range of the quadratic function f(x) = -(x + 1)^2 - 2?

{y : y ≤ -2, y ∈ ℝ} Signup and view all the answers

What is the effect of shifting the equation of a parabola y = a(x + p)^2 + q, m units to the left?

Replace x with x - m. Signup and view all the answers

What is the turning point of the graph of y = -(x - 1)^2 - 2?

(1, -2) Signup and view all the answers

What is the equation of a parabola that has x-intercepts at -2 and 4, and passes through the point (1, 3)?

y = (x + 2)(x - 4) Signup and view all the answers

What is the range of the quadratic function f(x) = (x + 2)^2 - 3?

{y : y ≥ -3, y ∈ ℝ} Signup and view all the answers

Gr 11 Math Ch 5: Quadratic Function

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Questions and Answers

What is the domain of a quadratic function?

What is the range of a quadratic function when a > 0?

How do you find the y-intercept of a quadratic function?

What is the turning point of the quadratic function f(x) = a(x + p)^2 + q?

What is the axis of symmetry of the quadratic function f(x) = a(x + p)^2 + q?

How do you shift the graph of a parabola m units to the right?

What is the equation of a parabola that passes through the points (x1, 0) and (x2, 0)?

What is the equation of a parabola that has a turning point (p, q) and passes through the point (r, s)?

What is the effect of $q$ on the graph of $y = ax^2 + q$?

What is the effect of $a$ on the graph of $y = ax^2 + q$ when $a > 0$?

What is the effect of $p$ on the graph of $y = a(x + p)^2 + q$?

What is the axis of symmetry of the graph of $y = a(x + p)^2 + q$?

What type of graph does $y = ax^2 + q$ represent when $a > 0$?

What is the y-intercept of the graph of $y = ax^2 + q$?

What happens to the graph of $y = ax^2 + q$ when $a$ gets closer to 0?

What type of graph does $y = a(x + p)^2 + q$ represent when $a < 0$?

What is the effect of a negative value of q on the graph of y = ax^2 + q?

What happens to the graph of y = a(x + p)^2 + q when the value of p increases?

What is the shape of the graph of y = ax^2 + q when a is negative?

What is the turning point of the graph of y = a(x + p)^2 + q when a is positive?

What happens to the graph of y = ax^2 + q when the value of a gets closer to 0?

What is the effect of a positive value of q on the graph of y = ax^2 + q?

What is the turning point of the graph of y = a(x + p)^2 + q when a is negative?

What happens to the graph of y = a(x + p)^2 + q when the value of a gets smaller?

What is the effect of shifting the equation of a parabola y = ax^2 + q, q units down?

What is the form of the axis of symmetry for the graph of y = a(x + p)^2 + q?

What is the turning point of the graph of y = a(x - p)^2 + q?

What information is required to find the equation of a parabola in the form y = a(x - x1)(x - x2)?

What is the effect of shifting the equation of a parabola y = ax^2, m units to the left?

What is the form of the equation of a parabola that has a turning point (p, q) and passes through the point (r, s)?

What is the y-intercept of the graph of y = ax^2 + q?

What is the effect of shifting the equation of a parabola y = a(x + p)^2 + q, n units up?

What is the effect of increasing the value of $p$ on the graph of $y = a(x + p)^2 + q$?

What is the shape of the graph of $y = ax^2 + q$ when $a$ is negative?

What is the effect of decreasing the value of $a$ on the graph of $y = a(x + p)^2 + q$?

What is the axis of symmetry of the graph of $y = a(x + p)^2 + q$?

What is the effect of $q$ on the graph of $y = ax^2 + q$ when $q > 0$?

What is the effect of increasing the value of $a$ on the graph of $y = ax^2 + q$?

What is the turning point of the graph of $y = a(x + p)^2 + q$ when $a > 0$?

What is the effect of decreasing the value of $q$ on the graph of $y = ax^2 + q$?

What is the range of the quadratic function f(x) = a(x + p)^2 + q if a < 0?

If the graph of a quadratic function has a turning point at (-2, 3), what is the corresponding equation of the quadratic function in the form f(x) = a(x + p)^2 + q?

What is the effect of shifting the graph of y = ax^2 + q, 2 units to the right?

What is the equation of a parabola that has x-intercepts at 2 and 4, and passes through the point (3, 5)?

If the graph of a quadratic function has a y-intercept at (0, 2), what is the corresponding equation of the quadratic function in the form f(x) = a(x + p)^2 + q?

What is the effect of shifting the equation of a parabola y = ax^2, 3 units down?

What is the axis of symmetry of the graph of y = a(x + 2)^2 + 3?

What is the equation of a parabola that passes through the points (1, 0) and (3, 0), and has a turning point at (2, 4)?

What is the effect of a large value of a on the graph of y = ax^2 + q?

What is the effect of p on the turning point of the graph of y = a(x + p)^2 + q?

What is the effect of q on the graph of y = ax^2 + q when q is negative?

What is the shape of the graph of y = ax^2 + q when a is positive?

What is the axis of symmetry of the graph of y = a(x + p)^2 + q?

What is the effect of a negative value of a on the graph of y = ax^2 + q?

What is the effect of increasing the value of p on the graph of y = a(x + p)^2 + q?

What is the effect of decreasing the value of a on the graph of y = ax^2 + q?

What is the effect of a negative value of a on the graph of y = a(x + p)^2 + q?

What is the equation of a parabola that has a turning point at (-1, 2) and passes through the point (0, 4)?

What is the axis of symmetry of the graph of y = a(x - 2)^2 + 3?

What is the range of the quadratic function f(x) = -(x + 1)^2 - 2?

What is the effect of shifting the equation of a parabola y = a(x + p)^2 + q, m units to the left?

What is the turning point of the graph of y = -(x - 1)^2 - 2?

What is the equation of a parabola that has x-intercepts at -2 and 4, and passes through the point (1, 3)?

What is the range of the quadratic function f(x) = (x + 2)^2 - 3?

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