Quadratic Equations

Trinomial

A polynomial with three terms

Binomial

A polynomial with two terms

Roots/Zeroes/Solutions

Can be found where the graph crosses the x-axis

Quadratic Equation

Polynomial with degree 2

A quadratic equation will have two solutions when...

The graph crosses the x axis in two places

Parabola

The shape of a the graph of a quadratic function

Formula for the discriminant

b^2-4ac

The discriminant tells you...

how many solutions a quadratic equation has.

definition of axis of symmetry

the line that cuts the graph into two symmetrical parts

A quadratic equation will have no real solutions when...

the parabola does not cross the x axis

y intercept

the point where the graph crosses the y axis

A quadratic equation will have one solution when...

the vertex of the parabola is on the x axis

Solve (x + 10)(x + 2) = 0

x = -10, x = -2

Solve (x + 5)(x - 1) = 0

x = -5, x = 1

Formula for the axis of symmetry

x = -b/2a

Solve (x - 10)(x - 2) = 0

x = 2, x = 10

Solve (x - 5)(x + 1) = 0

x = 5, x = -1

Factor x^2 + 20x + 100

(x + 10)(x + 10)

Factor x^2 + 10x + 25

(x + 5)(x + 5)

Factor x^2 - 20x + 100

(x - 10)(x - 10)

Factor x^2 - 10x + 25

(x - 5)(x - 5)

To make x^2 + 10x + _____ a perfect square trinomial, add

25

To make x^2 + 50x + _____ a perfect square trinomial, add

625

To make x^2 -6x + _____ a perfect square trinomial, add

9

Standard Form

This quadratic function is written in ...

Vertex Form

This quadratic function is written in....