# Quadratic Functions

by
**aarthur**

Last updated 8 years ago

** Discipline: **

Math ** Subject: **

Algebra I
** Grade:**

8

Quadratic Functions Project

Vertex: (1,0)Axis of Symmetry: -1Solutions: 1 Y-Intercept: 2Domain: All Real NumbersRange: Y ≥ 0

Vertex: (2, 32)Axis of Symmetry: 2Solutions: -2 & 6Y-Intercept: 24Domain: All Real NumbersRange: Y ≤ 32

-2x² +8x+24

2x²-4x+2

To find the Axis of Symmetry, you use the equation -b2a

You can use this Axis of symmetry value to find the vertex by plugging it into the equation.

2(1)²-4(1)+22(1)-4+22-4+20Vertex is (1,0)

-2(2)²+8(2)+24-2(4)+16+24-8+16+2432Vertex is (2,32)

You can tell if a parabola will open upward or downward by looking at the "a" value. If the "a" value is negative, the parabola will open downward. If the "a" value is positive, the parabola will open upward. For example an "a" value of 2 would open upward but an "a" value of -2 would open downward.

For this equation the problem would be -(-4) 4 12(2) 4 1 This is your axis of symmetry.

For this equation the problem would be-(8) -8 22(-2) -4 1 This is your axis of symmetry.

Real Life Examples of Parabolas

Find Solutions by factoring:2x²-4x+2M A-2,-2 -42x(x-1) 1(x-1)(2x-2) (x-1) +2 +12x=2 x=1 x=1

Find Solutions by Factoring:-2x² +8x+24M A -4,12 8-2x(x+2) 12(x+2)(-2x+12) (x+2) -12 -2-2x=-12x=6 x=-2

Find Solutions by Factoring

A water fountain is also a maximum parabola because the water is shot into the air, and it falls back to the ground once it reaches its maximum point.

A rainbow is a maximum parabola because it comes to a rounded point at the top and goes down on either side.

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