Gr 10 Math Ch 5: Quadratic Functions

What is the range of the function when the coefficient of $x^2$ is negative?

All real numbers

($- ext{∞}; q]$ (correct)

[q; $+ ext{∞}$)

($q; + ext{∞}$)

At which point does the turning point of the graph occur when $a > 0$?

(0, q) (correct)

($ ext{∞}$, $q$)

(0, 0)

(q, 0)

How can you find the y-intercept of the function $y = ax^2 + q$?

By setting $y = 0$

By setting $a = 0$

By setting $x = 0$ (correct)

By calculating the limit as $x$ approaches $ ext{∞}$

What does a positive value of $a$ indicate about the graph of the function?

The graph is a 'smile' shape. Signup and view all the answers

What is the axis of symmetry for the function of the form $f(x) = ax^2 + q$?

The line $x = 0$ Signup and view all the answers

Which statement is true about the x-intercepts of the function $y = ax^2 + q$?

They can be found by setting $y = 0$. Signup and view all the answers

What happens to the graph of the function when the value of q is greater than 0?

It shifts upward by q units. Signup and view all the answers

If the coefficient a is negative, what shape will the graph of the function take?

It will form a frown. Signup and view all the answers

How does a value of a that is between 0 and 1 affect the graph of the function?

The graph becomes wider. Signup and view all the answers

Which point indicates the turning point of the function when a is greater than 0?

(0, q) Signup and view all the answers

What effect does a value of q less than 0 have on the graph?

It slides the graph downwards. Signup and view all the answers

If a is equal to -1, what is true about the graph's shape?

The graph will be a downward-opening parabola with a specific width. Signup and view all the answers

What is the domain of any parabolic function in standard form?

All real numbers. Signup and view all the answers

Which of the following is a characteristic of a parabola when a is greater than 0?

It opens upwards and has a minimum turning point. Signup and view all the answers

How does a positive value of q affect the graph of the function y = ax^2 + q?

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

What occurs when the value of a is greater than 0 in the function y = ax^2 + q?

The graph resembles a 'smile'. Signup and view all the answers

If a is less than 0, what shape does the graph of the function y = ax^2 + q take?

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

For values of a between -1 and 0, how does this affect the width of the parabola?

The graph becomes narrower as a approaches 0. Signup and view all the answers

What is the behavior of the graph when q is equal to 0?

The turning point is on the x-axis. Signup and view all the answers

In the function y = ax^2 + q, what is the domain of the parabola?

All real numbers. Signup and view all the answers

How does the value of q affect the turning point of the graph when q is negative?

The turning point moves down to (0, -q). Signup and view all the answers

What happens to the parabola when the value of a is between 0 and 1?

The graph becomes wider as a approaches 0. Signup and view all the answers

What determines the direction of the parabola in the function $y = ax^2 + q$?

The value of $a$ Signup and view all the answers

Given a function $f(x) = ax^2 + q$, if $a < 0$, what can be said about the range of the function?

The range is $(- ext{infinity}; q]$. Signup and view all the answers

If the function $f(x) = ax^2 + q$ has a minimum turning point, which of the following must be true?

The value of $a$ is greater than zero. Signup and view all the answers

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

It is the point where the graph crosses the y-axis. Signup and view all the answers

Which of the following statements is true about the axis of symmetry for the function $f(x) = ax^2 + q$?

It is the vertical line $x = 0$. Signup and view all the answers

For which scenario would the graph of $y = ax^2 + q$ result in a 'frowning' shape?

When $a$ is negative and $q$ is positive. Signup and view all the answers

What is the result when the coefficient $a$ is positive in terms of the graph's behavior?

The graph will open upwards forming a parabola. Signup and view all the answers

Which statement about the range of the function $y = ax^2 + q$ is accurate when $q$ is negative and $a$ is positive?

The range is $[q; ext{infinity})$. Signup and view all the answers

What are the coordinates of the turning point for the function $f(x) = ax^2 + q$ when $a < 0$?

(0, q) Signup and view all the answers

If the function $y = ax^2 + q$ has an axis of symmetry at $x = 0$, which of the following must be true?

The graph is symmetrical about the y-axis. Signup and view all the answers

In a function of the form $f(x) = ax^2 + q$, what do the x-intercepts indicate?

They represent the input values where the output is zero. Signup and view all the answers

What is represented by the y-intercept in the function $y = ax^2 + q$?

The value of q when x is zero. Signup and view all the answers

What effect does a positive integer value of q have on the graph of the function y = ax^2 + q?

It shifts the entire graph vertically upwards, with the turning point at (0, q). Signup and view all the answers

If a is negative and greater than -1 in the function y = ax^2 + q, what is the appearance of the graph?

The graph appears wider, showing a gentle bottom curve. Signup and view all the answers

Which statement is true when the value of a is between 0 and 1?

The parabola widens as a approaches 0, indicating a less steep shape. Signup and view all the answers

How does a negative value of q affect the graph of the function y = ax^2 + q when a is also negative?

It vertically shifts the graph downwards, positioning the turning point below the y-axis. Signup and view all the answers

What effect does increasing the absolute value of a have on the shape of the graph for a > 0?

The graph becomes narrower as the maximum point moves higher. Signup and view all the answers

Which effect does a change in the sign of a have on the graph of y = ax^2 + q?

The direction of the opening of the parabola changes from up to down or vice versa. Signup and view all the answers

What describes the domain of any quadratic function in the form y = ax^2 + q?

It includes all real numbers with no restrictions. Signup and view all the answers

If q is equal to 0 in the function y = ax^2 + q, how does it affect the turning point?

The turning point remains on the x-axis regardless of the value of a. Signup and view all the answers

What is the range of the function when the coefficient of $x^2$ is positive and $q$ is 5?

[5; , \infty) Signup and view all the answers

When does the graph of the function $y = ax^2 + q$ change from a 'smile' to a 'frown' shape?

When $a$ changes from positive to negative Signup and view all the answers

What characteristic is common in all parabolic graphs of the form $f(x) = ax^2 + q$?

They are symmetric with respect to the y-axis. Signup and view all the answers

For a quadratic function $y = ax^2 + q$, how can one determine the x-intercepts?

By finding the values of $x$ that satisfy $ax^2 + q = 0$ Signup and view all the answers

If the function $y = ax^2 + q$ has a maximum turning point, which of the following must be true about $a$?

$a$ is less than 0 Signup and view all the answers

In the context of the function $y = ax^2 + q$, which statement is accurate regarding the turning point and its relationship with $q$?

The y-coordinate of the turning point is equal to $q$. Signup and view all the answers

How does increasing the absolute value of the coefficient $a$ affect the appearance of the graph when $a > 0$?

The graph gets narrower and maintains a minimum turning point. Signup and view all the answers

What is the impact of a negative value of $q$ on the turning point of the graph when $a < 0$?

The turning point shifts downwards to a position below the x-axis. Signup and view all the answers

What can be inferred about the graph's shape when $-1 < a < 0$?

The graph becomes wider and retains a maximum turning point. Signup and view all the answers

When the coefficient $a$ is between 0 and 1, what effect occurs on the width of the parabolic graph?

The graph widens as $a$ approaches 0. Signup and view all the answers

If the function $y = ax^2 + q$ results in a 'smiling' shape, which must be true about $a$ and $q$?

$a$ must be positive while $q$ can be any value. Signup and view all the answers

In what scenario will a parabolic graph with $a < 0$ have a maximum turning point at (0; q)?

If $q$ is greater than or equal to 0. Signup and view all the answers

What change occurs to the graph of $y = ax^2 + q$ if $q$ is set to a positive value?

The entire graph shifts upwards by $q$ units. Signup and view all the answers

What does the domain of any quadratic function in the form $y = ax^2 + q$ signify?

It includes all real numbers without restrictions. Signup and view all the answers