Question 1

What is the length of the segment connecting the points $$(-3, 7)$$ and $$(-9, 4)$$?

Accepted Answer

$$\sqrt{45} = 3\sqrt{5}$$

Question 2

What is the midpoint of the segment connecting $$(-3, 7)$$ and $$(-9, 4)$$?

Accepted Answer

$$(-6, 5.5)$$

Question 3

Write the equation of a circle with center $$(0, -5)$$ and radius $$7.$$

Accepted Answer

$$(x-0)^2$$ + $$(y+5)^2 = 49$

Question 4

Given the endpoints of a diameter $$(-9, 2)$$ and $$(1, 4)$$, what is the equation of the circle?

Accepted Answer

$$(x+4)^2$$ + $$(y-3)^2 = 26$

Question 5

Determine the center and radius of the circle $$x^2$$ + $$y^2 - 10x + 4y - 9 = 0$.

Accepted Answer

Center: $$(5, -2)$$, Radius: $$\sqrt{38}$$

Question 6

Which of the following points lies on the circle $$x^2$$ + $$y^2 = 100$?

Accepted Answer

$$(9, 3)$$

Question 7

Write the equation of a parabola with a maximum value of $$-7 at$$ $$x=5$$ and passing through $$(3, -19). $$Leave your answer in vertex form.

Accepted Answer

$$y = -3(x-5)^2$ - 7$$

Question 8

An object is thrown vertically upward from a 240-foot building. Its height $$h in $$feet after $$t$$ seconds is modeled by $$h(t) = -16t^2$ + 64t + 240. $$What is the maximum height reached by the object?

Accepted Answer

$$336$$ feet

Question 9

Given $$y = -2x^2$ - 4x + 1$$, what are the coordinates of the vertex?

Accepted Answer

$$(-1, 3)$$

Question 10

For the quadratic $$y = -2x^2$ - 4x + 1$$, what is the axis of symmetry?

Accepted Answer

$$x = -1$$

Question 11

You have a 500-foot roll of fencing and want to fence a rectangular playground with a divider down the middle (as shown in the first image). What are the dimensions of the largest possible area you can enclose?

Accepted Answer

$$L = 125 ft$$, $$w = 100 ft$$

Question 12

What is the largest area you can enclose with a 500-foot roll of fencing and a divider down the middle (as shown in the first image)?

Accepted Answer

$$12,500 ft$^2$$

Question 13

Factor $$x^2 - 13x - 30$.

Accepted Answer

$$(x-15)(x+2)$$

Question 14

Factor $$x^2 - 9$.

Accepted Answer

$$(x-3)(x+3)$$

Question 15

Write the equation of the circle whose diameter has endpoints $$(-5, 3)$$ and $$(-7, 33).$$

Accepted Answer

$$(x+6)^2$$ + $$(y-18)^2 = 260$

Question 16

Rewrite $$y = x^2$ - 8x + 10 in $$vertex form. What is the vertex?

Accepted Answer

$$y = (x-4)^2$ - 6$$, Vertex: $$(4, -6)$$

Question 17

Given the parabola $$y = 3(x+1)(x-5)$$, what information is easily obtained from this form?

Accepted Answer

The $$x-$$intercepts

Question 18

Rewrite $$y = 3(x+1)(x-5) in $$standard form.

Accepted Answer

$$y = 3x^2$ - 12x - 15$$

Circle and Parabola Test Practice Problems – Step-by-Step Precalculus Guidance

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