Question 1

Given the quadratic function $$f(x) = 2x^2$ - 16x + 37$$, what are the coordinates of the vertex of its graph?

Accepted Answer

$$(4, 5)$$

Question 2

For the function $$f(x) = 2x^2$ - 16x + 37$$, which of the following best describes the direction in which the parabola opens and the location of its vertex?

Accepted Answer

Opens upward; vertex at $$(4, 5)$$

Question 3

A company models its profit with the function $$P(x) = 2x^2$ - 16x + 37$$, where $$x is $$the number of units produced (in thousands). What production level $$x$$ maximizes or minimizes the profit, and what is the corresponding profit?

Accepted Answer

Minimum profit at $$x = 4$$, $$P(4) = 5$$

Question 4

Which of the following is the correct process to find the vertex of $$f(x) = 2x^2$ - 16x + 37$$?

Accepted Answer

Use $$x = -\frac{b}{2a} to $$find $$x$$, then substitute into $$f(x)$$ for $$y$$

Question 5

If the vertex of $$f(x) = 2x^2$ - 16x + 37 is$$ $$(h, k)$$, what are the values of $$h$$ and $$k$$?

Accepted Answer

$$h = 4$$, $$k = 5$$

Question 6

Which of the following is the axis of symmetry for the graph of $$f(x) = 2x^2$ - 16x + 37$$?

Accepted Answer

$$x = 4$$

Question 7

Suppose $$f(x) = 2x^2$ - 16x + 37$$ models the height (in meters) of a projectile at time $$x$$ seconds. At what time does the projectile reach its minimum height, and what is that height?

Accepted Answer

At $$x = 4$$ seconds, height is $$5$$ meters

Question 8

Which of the following is the completed square form of $$f(x) = 2x^2$ - 16x + 37$$?

Accepted Answer

$$f(x) = 2(x - 4)^2$ + 5$$

Question 9

If the minimum value of $$f(x) = 2x^2$ - 16x + 37 is$$ $$k$$, what is $$k$$?

Accepted Answer

$$5$$

Question 10

Which of the following statements is true about the graph of $$f(x) = 2x^2$ - 16x + 37$$?

Accepted Answer

The vertex is a minimum point at $$(4, 5)$$

Finding the Vertex of a Quadratic Function

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