Solving Quadratic Equations

Factoring

100

Solve the following quadratic equation. 

(x - 7)(x + 2) = 0

x = 7 x = -2 

or x = { 7, -2}

200

Solve the following quadratic equation by factoring.

 x² - 6x - 27 = 0

x = 9 x = -3

300

Solve the following quadratic equation by factoring. 2x² - 5x - 3 = 0

x = -1/2 x = 3

Quadratic Facts

100

When solving quadratic equations, we are trying to find what feature of the parabola?

x-intercepts

200

Why is the quadratic formula useful for solving quadratic equations?

We can ALWAYS use the quadratic formula, but we cannot always factor.

300

How do we know a quadratic function does not have a real number solution when using the quadratic formula?

The number under the square root is negative

Graphing

100

What is the name of the graph for quadratic equations?

A parabola

200

This line crosses the vertex of a parabola and divides the parabola into 2 equal halves.

Axis of Symmetry

300

This point is the center of a parabola and can be a maximum or minimum, depending on the direction of the parabola.

Vertex

Quadratic Formula

100

Identify a, b and c in the following equation: 

x² + 6x - 5 = 0

a = 1; b = 6; c = -5

200

Identify a, b and c in the following equation: 

x² - 9x + 20 = 9

a = 1; b = -9; c = 11

300

What is the quadratic formula?

x=(-b +- sqrt(b^2-4ac))/(2a)