Basics
A quadratic is an equation or formula in which a variable is squared.
(In the equation above, the variable x is squared.)
A question involving quadratics could involve a relatively simple plug-in, where you plug in a number for x to solve for y using the quadratic equation.
A question involving quadratics could involve more complicated calculations, where you must solve for x using the quadratic formula.
Because the quadratic formula features ± calculations, in most cases you will produce two answers for x.
When squaring a negative number, remember to use parentheses to protect the order of operations.
Formulas (Mathematics Formula Sheet)
standard form of a quadratic equation
y =
quadratic formula
x =
Formulas (NOT on Mathematics Formula Sheet)
quadratic formula
x = means —>
“
OR
Question
For the quadratic equation y = 4x² – 18x + 20, solve for y when x = 3.
Answer
y = 2
Answer Process
See Plug-In.
y = 4x² – 18x + 20
y = 4 × 3² – 18 × 3 + 20 = 2
Input | Display | Comment |
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blinker | clears screen |
4 × 3 ![]() |
4*3²-18*3+20 | y = 4x² – 18x + 20 Plug in 3 for x. |
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2 | Answer |
Quadratics |
Question
For the quadratic equation y = 4x² – 18x + 20, solve for y when x = -3.
Answer
y = 110
Answer Process
See Plug-In.
y = 4x² – 18x + 20
y = 4 × (-3)² – 18 × -3 + 20 = 110
Input | Display | Comment |
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blinker | clears screen |
4 × ![]() ![]() ![]() – 18 × -3 + 20 |
4*(-3)²-18*-3+20 | y = 4x² – 18x + 20 Plug in -3 for x. Parentheses protect order of operations. |
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110 | Answer |
Quadratics |
Question
For the quadratic equation 2x² – 9x + 4 = 0, solve for x.
Answer
x = and x = 4
Answer Process
quadratic formula
x =
ax² + bx + c = 0
2x² – 9x + 4 = 0
a = 2
b = -9
c = 4
= 4
OR
=
Input | Display | Comment |
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blinker | clears screen |
![]() ![]() ![]() ![]() ![]() ![]() – 4 × 2 × 4 ![]() ![]() |
||
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4 | Answer |
![]() ![]() ![]() ![]() ![]() ![]() – 4 × 2 × 4 ![]() ![]() |
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Answer | |
Quadratics |
Practice – Questions
1. For the quadratic equation y = x² + 6x + 8, solve for y when x = 2.
2. For the quadratic equation y = x² + 6x + 8, solve for y when x = -2.
3. For the quadratic equation y = 6x² – 18x + 12, solve for y when x = 4.
4. For the quadratic equation y = 6x² – 18x + 12, solve for y when x = -4.
5. For the quadratic equation 3x² – 7x + 4 = 0, solve for x.
Practice – Answers
1. y = 24
2. y = 0
3. y = 36
4. y = 180
5. x = 1 or x =