Q: If $f(x) = -x^2 - 4x + 3$ models the height of a projectile, at what time does it hit the ground?

$x = -5$ \, \text{or} \, x = 1$

Question 1

Given the quadratic function $f(x) = -x^2 - 4x + 3$, what are the coordinates of the vertex?

Accepted Answer

$(-2, 7)$

Question 2

For the function $f(x) = -x^2 - 4x + 3$, what is the axis of symmetry?

Accepted Answer

$x = -2$

Question 3

Which of the following describes the direction in which the parabola $f(x) = -x^2 - 4x + 3$ opens?

Accepted Answer

Downward

Question 4

What is the maximum value of $f(x) = -x^2 - 4x + 3$?

Accepted Answer

$7$

Question 5

Rewrite $f(x) = -x^2 - 4x + 3$ in vertex form.

Accepted Answer

$f(x) = -(x + 2)^2 + 7$

Question 6

If the quadratic function $f(x) = -x^2 - 4x + 3$ models the height (in meters) of a ball thrown from a building, what is the initial height of the ball?

Accepted Answer

$3$ meters

Question 7

Which value of $x$ gives the maximum value for $f(x) = -x^2 - 4x + 3$?

Accepted Answer

$x = -2$

Question 8

What are the $x$-intercepts of the function $f(x) = -x^2 - 4x + 3$?

Accepted Answer

$x = -5$ and $x = 1$

Question 9

Suppose $f(x) = -x^2 - 4x + 3$ represents the profit (in thousands of dollars) for a company, where $x$ is the number of units produced. How many units should be produced to maximize profit?

Accepted Answer

$-2$ units

Question 10

Which of the following is the correct method to find the vertex of $f(x) = ax^2 + bx + c$?

Accepted Answer

Set $x = -\frac{b}{2a}$ and calculate $f(x)$

Question 11

If the vertex of a parabola is at $(-2, 7)$, which of the following could be its equation?

Accepted Answer

$f(x) = -(x + 2)^2 + 7$

Question 12

For $f(x) = -x^2 - 4x + 3$, what is the range of the function?

Accepted Answer

$(-\infty, 7]$

Question 13

If the graph of $f(x) = -x^2 - 4x + 3$ is shifted 3 units up, what is the new vertex?

Accepted Answer

$(-2, 10)$

Question 14

Which transformation occurs when $f(x) = -x^2 - 4x + 3$ is replaced by $f(x) = -x^2 - 4x - 2$?

Accepted Answer

The graph shifts down by 5 units

Question 15

If $f(x) = -x^2 - 4x + 3$ models the height of a projectile, at what time does it hit the ground?

Accepted Answer

$x = -5$ \, 	ext{or} \, x = 1$

Question 16

What is the discriminant of $f(x) = -x^2 - 4x + 3$ and what does it tell you about the graph?

Accepted Answer

$D = (-4)^2 - 4(-1)(3) = 16 + 12 = 28$, so the parabola has two real $x$-intercepts

Question 17

If the vertex of $f(x) = -x^2 - 4x + 3$ is $(-2, 7)$, what is the minimum value of the function?

Accepted Answer

$-\infty$

Question 18

Which of the following statements is true about the graph of $f(x) = -x^2 - 4x + 3$?

Accepted Answer

It has a maximum at $x = -2$

Question 19

If $f(x) = -x^2 - 4x + 3$ is reflected over the $x$-axis, what is the equation of the new function?

Accepted Answer

$f(x) = x^2 + 4x - 3$

Quadratic Functions: Finding the Vertex of a Parabola

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