Gr 10 Math Ch 5: Quadratic Functions

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Questions and Answers

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?

<p>The graph is a 'smile' shape. (C)</p> Signup and view all the answers

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

<p>The line $x = 0$ (A)</p> Signup and view all the answers

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

<p>They can be found by setting $y = 0$. (D)</p> Signup and view all the answers

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

<p>It shifts upward by q units. (C)</p> Signup and view all the answers

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

<p>It will form a frown. (A)</p> Signup and view all the answers

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

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

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

<p>(0, q) (B)</p> Signup and view all the answers

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

<p>It slides the graph downwards. (A)</p> Signup and view all the answers

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

<p>The graph will be a downward-opening parabola with a specific width. (B)</p> Signup and view all the answers

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

<p>All real numbers. (D)</p> Signup and view all the answers

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

<p>It opens upwards and has a minimum turning point. (A)</p> Signup and view all the answers

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

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

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

<p>The graph resembles a 'smile'. (B)</p> 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?

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

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

<p>The graph becomes narrower as a approaches 0. (B)</p> Signup and view all the answers

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

<p>The turning point is on the x-axis. (D)</p> Signup and view all the answers

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

<p>All real numbers. (B)</p> Signup and view all the answers

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

<p>The turning point moves down to (0, -q). (B)</p> Signup and view all the answers

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

<p>The graph becomes wider as a approaches 0. (D)</p> Signup and view all the answers

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

<p>The value of $a$ (C)</p> 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?

<p>The range is $(- ext{infinity}; q]$. (C)</p> 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?

<p>The value of $a$ is greater than zero. (A)</p> Signup and view all the answers

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

<p>It is the point where the graph crosses the y-axis. (C)</p> Signup and view all the answers

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

<p>It is the vertical line $x = 0$. (D)</p> Signup and view all the answers

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

<p>When $a$ is negative and $q$ is positive. (D)</p> Signup and view all the answers

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

<p>The graph will open upwards forming a parabola. (A)</p> 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?

<p>The range is $[q; ext{infinity})$. (B)</p> Signup and view all the answers

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

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

<p>The graph is symmetrical about the y-axis. (C)</p> Signup and view all the answers

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

<p>They represent the input values where the output is zero. (D)</p> Signup and view all the answers

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

<p>The value of q when x is zero. (B)</p> 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?

<p>It shifts the entire graph vertically upwards, with the turning point at (0, q). (A)</p> 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?

<p>The graph appears wider, showing a gentle bottom curve. (D)</p> Signup and view all the answers

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

<p>The parabola widens as a approaches 0, indicating a less steep shape. (D)</p> 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?

<p>It vertically shifts the graph downwards, positioning the turning point below the y-axis. (C)</p> 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?

<p>The graph becomes narrower as the maximum point moves higher. (D)</p> 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?

<p>The direction of the opening of the parabola changes from up to down or vice versa. (C)</p> Signup and view all the answers

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

<p>It includes all real numbers with no restrictions. (B)</p> 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?

<p>The turning point remains on the x-axis regardless of the value of a. (A)</p> 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?

<p>[5; , \infty) (B)</p> 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?

<p>When $a$ changes from positive to negative (A)</p> Signup and view all the answers

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

<p>They are symmetric with respect to the y-axis. (A)</p> Signup and view all the answers

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

<p>By finding the values of $x$ that satisfy $ax^2 + q = 0$ (C)</p> 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 $a$?

<p>$a$ is less than 0 (C)</p> 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 $q$?

<p>The y-coordinate of the turning point is equal to $q$. (B)</p> Signup and view all the answers

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

<p>The graph gets narrower and maintains a minimum turning point. (B)</p> Signup and view all the answers

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

<p>The turning point shifts downwards to a position below the x-axis. (A)</p> Signup and view all the answers

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

<p>The graph becomes wider and retains a maximum turning point. (A)</p> 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?

<p>The graph widens as $a$ approaches 0. (B)</p> 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 $q$?

<p>$a$ must be positive while $q$ can be any value. (D)</p> Signup and view all the answers

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

<p>If $q$ is greater than or equal to 0. (A)</p> 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?

<p>The entire graph shifts upwards by $q$ units. (B)</p> Signup and view all the answers

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

<p>It includes all real numbers without restrictions. (A)</p> Signup and view all the answers

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