Quadratic Functions

A Quadratic Functions is a parabola whose axis of symmetry is parallel to the y - axis.

U - Shaped

Parabola

Concave up

Vertex

- If a graph is concave up, then the vertex is minimum value. (lowest point on graph)

- If the graph is concave down the vertex has maximum value.

- All graphs of quadratic functions have vertical symmetry

-Standard Form:

​f(x) = ax2 + bx + c

​a, b, c are constants

-Vertex Form:

​g(x) = a(x - h)2

​where (h, k) is the vertex

-Factoral form Form:

​h(x) = a(x - r) (x - s)

​where r and s are x- intercepts

- If the leading coefficent (first number of the function) is negative then the graph is concve down and there is a max value.

- If the leading coefficent is positive then the graph is concave up and there is a minimum value.

Ex 1.

F(x) = x2 - x - 6

Find x and y intercept

y-int:

when x=0 , y=-6

(0,-6)

x-int:

0= x2 - x - 6

    (x - 3) (x + 2)

x = 3​x = 2

(3,0)​(-2,0)

-When the quadratic formula is not factorable we can use the quadratic function