**
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 (provided by Mathematics Formula Sheet)
**standard form of a quadratic equation

quadratic formula

**
Formulas (NOT provided by Mathematics Formula Sheet)
**quadratic formula

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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

Calculator Click |
What You See |
Comment |

blinker | clears screen | |

4 × 3 – 18 × 3 + 20 | 4*3²-18*3+20 | y = 4x² – 18x + 20 Plug in 3 for x. |

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

Calculator Click |
What You See |
Comment |

blinker | clears screen | |

4 × -3 – 18 × -3 + 20 |
4*(-3)²-18*-3+20 | y = 4x² – 18x + 20 Plug in -3 for x. ## Parentheses protect order of operations. |

110 | Answer | |

## Quadratics |

Question

For the quadratic equation 2x² – 9x + 4 = 0, solve for x.

**Answer**

x = and x = 4

**Answer Process**

quadratic formula

ax² + bx + c = 0

2x² – 9x + 4 = 0

a = 2

b = -9

c = 4

= 4

OR

=

Calculator Click |
What You See |
Comment |

blinker | clears screen | |

– -9 + -9 – 4 × 2 × 4 2 × 2 |
||

4 | Answer | |

– -9 – -9 – 4 × 2 × 4 2 × 2 |
||

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 =