Unit 8 Test Review

A quadratic function is any function that can be placed in the form  $y=ax^2+bx+c$  , where  $a\ne0$  but b and c can be 0

Quadratic functions have the shape of a parabola (U-shaped graph) 

The parabola of a quadratic function will open upwards if  $a>0$  

This type of a quadratic will have a minimum y-value

The parabola of a quadratic function will open downwards if   $a<0$  

This type of parabola will have a maximum value

Vertex Form:  $f\left(x\right)=a\left(x-h\right)^2+k$  

a is the leading coefficient

h is the horizontal shift (opposite of what you see)

k is the vertical shift

Vertex:  $\left(opposite\ of\ h,\ k\right)$  

Parabolas are symmetrical!

Axis of Symmetry Formula:  $x=-\frac{b}{2a}$  

You can use this formula to find the vertex

If  $a>1$  , then the parabola is stretched

The larger the value of a, the more stretched the parabola is

If  $0<a<1$  , then the parabola is compressed

Compressed parabolas are wider

Find the zeros of quadratics algebraically by factoring

Make sure to set each part of the factored quadratic equal to 0