Gr 11 Math Ch 5: Quadratic Function
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Gr 11 Math Ch 5: Quadratic Function

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Questions and Answers

What is the domain of a quadratic function?

{x : x ∈ ℝ}

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

{y : y ≥ q, y ∈ ℝ}

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

Set x = 0

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

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

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

<p>x = -p</p> Signup and view all the answers

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

<p>Replace x with x - m</p> Signup and view all the answers

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

<p>y = a(x - x1)(x - x2)</p> 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)?

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

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

<p>It shifts the graph vertically.</p> Signup and view all the answers

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

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

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

<p>It shifts the graph horizontally.</p> Signup and view all the answers

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

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

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

<p>A 'smile' shape.</p> Signup and view all the answers

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

<p>The point $(0, q)$.</p> Signup and view all the answers

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

<p>The graph becomes wider.</p> Signup and view all the answers

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

<p>A 'frown' shape.</p> Signup and view all the answers

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

<p>The graph is shifted vertically downwards.</p> Signup and view all the answers

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

<p>The graph shifts to the right.</p> Signup and view all the answers

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

<p>A frown.</p> 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?

<p>A minimum turning point.</p> 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?

<p>The graph becomes wider.</p> Signup and view all the answers

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

<p>The graph is shifted vertically upwards.</p> 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?

<p>A maximum turning point.</p> 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?

<p>The graph becomes narrower.</p> Signup and view all the answers

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

<p>The graph is shifted q units up</p> 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?

<p>x = -p</p> Signup and view all the answers

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

<p>(p, q)</p> 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)?

<p>Y-intercept and x-intercepts</p> 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?

<p>Replace x with x - m</p> 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)?

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

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

<p>(0, q)</p> 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?

<p>Replace y with y + n</p> Signup and view all the answers

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

<p>The graph is shifted horizontally to the left.</p> Signup and view all the answers

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

<p>A parabola with a maximum turning point</p> Signup and view all the answers

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

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

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

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

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

<p>The graph is shifted vertically upwards.</p> Signup and view all the answers

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

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

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

<p>A minimum turning point</p> Signup and view all the answers

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

<p>The graph is shifted vertically downwards.</p> Signup and view all the answers

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

<p>All real numbers less than or equal to q</p> 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?

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

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

<p>Replace x with x + 2</p> 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)?

<p>y = a(x - 2)(x - 4)</p> 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?

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

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

<p>Replace y with y - 3</p> Signup and view all the answers

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

<p>x = -2</p> 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)?

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

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

<p>The graph becomes narrower</p> 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?

<p>It shifts the turning point to the right</p> Signup and view all the answers

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

<p>The graph shifts vertically downwards</p> Signup and view all the answers

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

<p>A 'smile' shape</p> Signup and view all the answers

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

<p>The line x = -p</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?

<p>The graph becomes a 'frown' shape</p> 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?

<p>The graph shifts to the right</p> Signup and view all the answers

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

<p>The graph becomes wider</p> 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?

<p>It opens downwards.</p> 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)?

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

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

<p>x = -2</p> Signup and view all the answers

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

<p>{y : y ≤ -2, y ∈ ℝ}</p> 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?

<p>Replace x with x - m.</p> Signup and view all the answers

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

<p>(1, -2)</p> 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)?

<p>y = (x + 2)(x - 4)</p> Signup and view all the answers

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

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

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