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

Study Guide - Practice Questions

Study Guide - Flashcards