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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