Math Core

This test covers the whole quadratics unit: graphing parabolas, vertex form, and solving quadratic equations by factoring, square roots, completing the square and the quadratic formula.

Question 1

The axis of symmetry of $y = 2x^2 - 12x + 5$ is the line $x = ?$

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 2

Find the vertex of $y = -x^2 + 6x - 4$ .

Enter a point like (2, -3)

Question 3

Find the range of $y = (x + 2)^2 - 7$ . Write it as an inequality in $y$ .

Enter an inequality, e.g. x >= 4, -2 < x <= 3, or x < 1 or x > 5

Question 4

Which equation matches the graph?

y = (x + 1)^2 - 4(-1, -4)(-3, 0)(1, 0)Open in grapher →

Question 5

A parabola has vertex $(4, -1)$ and passes through $(6, 7)$ . Its equation is $y = a(x - 4)^2 - 1$ . Find $a$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 6

Solve $x^2 - x - 20 = 0$ .

Separate answers with commas, e.g. 2, -5

Question 7

Solve $2x^2 + x - 6 = 0$ .

Separate answers with commas, e.g. 2, -5

Question 8

Solve $x^2 = 7x$ .

Separate answers with commas, e.g. 2, -5

Question 9

Solve $4x^2 - 100 = 0$ .

Separate answers with commas, e.g. 2, -5

Question 10

The equation $(x - 2)^2 = 11$ has two solutions. What is the larger one? Give an exact answer.

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 11

What number must be added to $x^2 - 16x$ to make a perfect square trinomial?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 12

Complete the square to write $y = x^2 + 4x + 1$ in the form $y = (x - h)^2 + k$ . What is $k$ ?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 13

How many real solutions does $2x^2 - 3x + 5 = 0$ have?

Question 14

Solve $x^2 + 2x - 4 = 0$ .

Question 15

A model rocket is launched from the ground. Its height in feet after $t$ seconds is $h(t) = -16t^2 + 96t$ . What is its maximum height, in feet?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.