Quiz: Attributes of Quadratic Functions

Sketch the axis of symmetry on the quadratic function shown at the right.

Now that you have sketched the axis of symmetry on the quadratic function shown at the right. Then write the equation for the axis of symmetry in the answer bank.

• x = -3

• x = -4

• y= -3

• y= -4

Find the vertex of the function g(x) = -3x² - 18x + 6.

• (-3, 33)

• (-3, -33)

• (3, 33)

• (3, -33)

What is the range of y = -x² + 8x - 14?

• y ≤ 4

• y ≤ 2

• all real numbers

• y ≥ 2

Which graph represents y = x² + 6x + 7?

• Graph A

• Graph B

• Graph C

• Graph D

Tags

CCSS.HSF-IF.C.7A

What are the zeros of graph B?

• -5 and 2

• 6.5

• 8

• -2 and 8

Answer explanation

The zeros of graph B are the x-values where the graph intersects the x-axis. In this case, the graph intersects at -5 and 2, making the correct answer -5 and 2.

Tags

CCSS.HSF-IF.C.7A

Which graph has a minimum of -2?

• Graph A only

• Graph B only

• Both A and C

• Graph C only

Tags

CCSS.HSF-IF.C.7A

Which of the following functions has an axis of symmetry equation of x = -2?

• y = 2x² + 16x + 30

• y = 3x² + 12x + 16

• Both a and b

• Neither a nor b

Answer explanation

The axis of symmetry for a quadratic function in the form y = ax² + bx + c is given by x = -b/(2a). For y = 3x² + 12x + 16, -b/(2a) = -12/(2*3) = -2. Thus, the correct choice is y = 3x² + 12x + 16.

Sheridan graphed the function f(x) = x² - 6x + 7. Which of the following will be true about Sheridan’s graph?

• The y-value of the vertex is -2.

• The equation for the axis of symmetry is x = 3.

• The vertex is located in Quadrant IV.

• All of the above are true.

Answer explanation

The vertex of f(x) = x² - 6x + 7 is at (3, -2). The axis of symmetry is x = 3, and the vertex is in Quadrant IV since the y-value is negative. Therefore, all statements are true.

Tags

CCSS.HSF-IF.C.7A

A quadratic function is shown on the graph. Which of the following statements are true?

I. The y-intercept is (0, -4).

II. The domain is all real numbers.

III. The range is y ≤ -4.

• I only

• II only

• I and II

• II and III

Answer explanation

Statement I is true as the graph shows the y-intercept at (0, -4). Statement II is also true since the domain of a quadratic function is all real numbers. Statement III is false; the range depends on the vertex, not just the y-intercept.

Tags

CCSS.HSF-IF.C.7A