Intro solving quads by graphing/factoring

​Solving Quadratics by Graphing and Factoring

By Francesca Donati

​Review: x-intercepts are where the graph crosses the x-axis! Remember that another name for x-intercepts are solutions, roots and zeros! We use these other names when solving for x.

For example, this graph has two x-intercepts, so it has TWO SOLUTIONS!

In particular, the two solutions are x=-2 and x=2

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For example, this graph has one x-intercept, so it has ONE SOLUTION!

In particular, the solution is x=1

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For example, this graph has NO x-intercept, so it has NO REAL SOLUTIONS!

Multiple Choice

• 1 Real Solution

• 2 Real Solutions

• No Real Solutions

• Half a Solution

Multiple Choice

How many solutions does the function have?

• No Real Solutions

• One Real Solution

• Two Real Solutions

• Four Real Solutions

Multiple Choice

How many solutions does the function have?

• No Real Solutions

• One Real Solution

• Two Real Solutions

• Four Real Solutions

Multiple Choice

• No Real Roots

• 1

• 2

• ∞

Multiple Choice

Name the x-intercept(s)?

• 0
• 4
• 2
• 0 and 4

Multiple Choice

Use the graph to determine the solutions.

• -1 and -3
• 1 and -3
• 1 and 3
• -1 and 3

Multiple Choice

What are the solutions?

• -2, 1
• 1, 2
• -1,2
• 0,-4

Multiple Choice

What is the greatest number of solutions that a Quadratic Equation can have?

• 0
• 1
• 2
• 3

Multiple Choice

When looking at a quadratic graph, the solution(s) are always the _____________.

• y-intercept

• vertex

• x-intercept(s)

• axis of symmetry

Remember that we can find the solutions from factored form using the Zero Product Property.

Multiple Choice

Solve using the zero product property

(x+2)(x-6)=0

• x=2, -6

• x=-2, -6

• x=-2, 6

• x=2, 6

Multiple Choice

Solve using the zero product property

(x-5)(x-10)=0

• x=5, 10

• x=-5, -10

• x=-5, 10

• x=5, -10

Multiple Choice

Solve using the zero product property

(x+13)(x+7)=0

• x=13, 7

• x=-13, -7

• x=-13, 7

• x=13, -7

Multiple Choice

Solve using the zero product property

(x-9)(x+1)=0

• x=9, 1

• x=-9, 1

• x=-9, -1

• x=9, -1

Multiple Choice

Solve using the zero product property

(x+5)(x-11)=0

• x=5, -11

• x=-5, -11

• x=-5, 11

• x=5, 11