Practice Quadratic Standard Form in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The standard form of a quadratic equation is ax2+bx+c=0ax^2 + bx + c = 0, where aโ‰ 0a \neq 0 and aa, bb, cc are real number coefficients.

Think of it as a template with three slots: aa controls the width and direction of the parabola, bb shifts it sideways, and cc slides it up or down. Every quadratic can be written this way by expanding and collecting like terms.

Showing a random 20 of 50 problems.

Example 1

medium
Find the xx-coordinate of the vertex of y=2x2โˆ’12x+7y = 2x^2 - 12x + 7 using standard form.

Example 2

easy
Identify aa, bb, cc in 3x2+5x+2=03x^2 + 5x + 2 = 0.

Example 3

challenge
Two quadratics x2+bx+c=0x^2 + bx + c = 0 share roots 22 and โˆ’3-3. Find bb and cc.

Example 4

medium
In standard form, what does the constant term cc represent on the graph?

Example 5

medium
Convert (2xโˆ’1)(x+3)=0(2x-1)(x+3) = 0 to standard form.

Example 6

easy
Is 5x+2=05x + 2 = 0 a quadratic equation?

Example 7

easy
Identify bb in 2x2โˆ’7x+3=02x^2 - 7x + 3 = 0.

Example 8

easy
Is 4xโˆ’x2+1=04x - x^2 + 1 = 0 in standard form? If not, rewrite it.

Example 9

easy
In x2+3xโˆ’10=0x^2 + 3x - 10 = 0, what is cc?

Example 10

easy
Write x2=9x^2 = 9 in standard form.

Example 11

easy
Write 3x2+2x=53x^2 + 2x = 5 in standard form.

Example 12

easy
Write 7xโˆ’2x2+5=07x - 2x^2 + 5 = 0 in standard form.

Example 13

medium
Convert y=2(xโˆ’1)(x+4)y = 2(x-1)(x+4) to standard form.

Example 14

challenge
A quadratic in standard form has a=1a=1, sum of roots 55, product of roots 66. Write it.

Example 15

medium
Does the parabola y=โˆ’3x2+xโˆ’1y = -3x^2 + x - 1 open up or down?

Example 16

hard
A quadratic in standard form has c=โˆ’12c = -12 and roots 33 and โˆ’4-4. Find the leading coefficient aa.

Example 17

easy
Identify cc in x2โˆ’6x=0x^2 - 6x = 0.

Example 18

hard
Given the parabola y=ax2+bx+cy = ax^2 + bx + c passes through (0,3)(0, 3), (1,0)(1, 0), and (โˆ’1,8)(-1, 8), find a,b,ca, b, c.

Example 19

medium
Expand 3(xโˆ’2)(x+1)3(x-2)(x+1) and write in standard form.

Example 20

hard
For what value of kk is kx2โˆ’4x+1=0kx^2 - 4x + 1 = 0 not a quadratic equation?