Module 11 Topic 1 Graphing and Solving Quadratic

EquationsGoal 4: The learner will use relations and

functions to solve problems and justify results.Objective 4.02: Graph, factor, and evaluate

quadratic functions to solve problems.

Graphs of Quadratic Equations are called

Parabolas

Vertex

Axis of Symmetry

y = ax2 + bx + c

Click on the parabola

below to watch a short clip on graphing quadratics.

a is a coefficient that determines if the parabola opens upward or downward

a, b and c are used to find the vertex using the following formula

Example 1: Determine if the parabola for the following functions open upward or downward.

a) y = x2 + 4x - 6

The graph opens upward because the value of a is 1 which is positive.

b) y = -3x2 + 6x – 2

The graph opens downward because the value of a is -3 which is negative.

Example 2: Find the Vertex

Let’s identify a, b and c Use the vertex formula to find the vertex.

y = x2 – 6x + 4

a = 1

b = -6

c = 4

Example 3: Find the Vertex when b = 0

Let’s identify a, b and c Use the vertex formula to find the vertex.

y = -3x2 + 6

a = -3

b = 0

c = 6

Solving Quadratic Equations can be done by factoring or graphing.

Set each factor equal to zero and solve for

x.y = x2 + 5x + 6

a = 1 b = 5 c = 6We need to find two factors that

have a product of 6 and a sum of 5.

So 2 and 3 will work for this problem.

Click on the parabolas to watch a short clip about solving quadratics.

2g3 =62 + 3 =5

y = (x + 2)(x + 3)

x + 2 = 0

x + 2 – 2 = 0 – 2

x = -2

x + 3 = 0

x + 3 – 3 = 0 - 3

x = -3

The quadratic equation crosses the x-axis at -2

and -3. These are called the roots, zeros, or

solutions.