Finding the X-Intercepts by Graphing and Factoring

Finding the X-Intercepts by Graphing and Factoring

What are x-intercepts?

• The place(s) where the graph touches the x-axis

• Occur when y = 0

• Also called solutions, roots or zeros

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Finding x-intercepts

• A quadratic function may have 1, 2 or no x-intercepts

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Finding x-intercepts by graphing

Find the x-intercepts by graphing

• Choose arbitrary values for x

• Evaluate the function for those values

• Plot the coordinates and draw a line connecting the points

• The place(s) where the graph touches the x-axis are the x-intercepts

• Remember that not all quadratic functions have x-intercepts

Solving Quadratic Functions by Factoring

Finding the x-intercepts by factoring

• Not all quadratic functions can be solved this way - only those that are factorable

• To find the x-intercepts, write the function in factored form

• f(x) = x² + x - 6 would be written as f(x) = (x-2)(x+3)

Finding the x-intercepts by factoring

• Remember that the x-intercepts are when y = 0

• Set f(x) = (x+3)(x-2) = 0

• The only way that a product can be zero is if one of its factors is zero

• Either (x+3) =0 or (x-2) = 0, or both

Finding the x-intercepts by factoring

• Set each factor = 0, and solve for x

• x + 3 = 0, x = -3

• x - 2 = 0, x = 2

• The x-intercepts are -3, 2

Find the x-intercepts (solutions, roots) of x² - 16x + 15

• 1. Factor x² - 16x + 15

• (Multiply 1 * 15 = 15)

• (Find the factors of 15 that add to -16) = -1, 15

• (Write x² - 1x - 15x + 16) = (x - 1)(x-15)

Find the x-intercepts (solutions, roots) of x² - 16x + 15

• 2. Set each factor = 0

• 3. (x - 1) = 0, x = 1

• 4. (x - 15) = 0, x = 15

• 5. The x-intercepts (roots, solutions) are 1 and 15

Find the x-intercepts (roots, solutions, zeros) of x² - x - 2

• 1. Find the factors of x² - x - 2

• (Multiply 1 * -2 = -2 )

• (Find the factors of -2 that add up to -1) = -2, 1

• (Rewrite x² - x -2 as x² + 1x - 2x - 2)

• (x+1)(x-2)

Find the x-intercepts (roots, solutions, zeros) of x² - x - 2

• 2. Set each factor = 0

• 3. x - 2 = 0, x = 2

• 4. x + 1 = 0, x = -1

• 5. The intercepts (zeros, roots, solutions) are 2 and -1

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Multiple Choice

If a quadratic function is represented as f(x) = (x - 7)(x + 8), find the zeroes.

• x = - 7 and x = 8

• x = 7 and x = -8

Multiple Choice

Which is a zero of the graph?

• 0

• -1

• 1.5

• -3

Multiple Choice

Factor the quadratic expression

d² - 10d + 25

• (d + 5) (d - 5)

• (d - 15) (d + 10)

• (d + 5) (d - 20)

• (d - 5) (d - 5)

Multiple Choice

Name the zeros?

• (0, 0)

• (2, 4)

• (0, 0) and (0, 4)

• (0, 0) and (4, 0)

Multiple Choice

Solve for the values of x:

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

• (5, 0) or (1, 0)

• (-5, 0) or (-1, 0)

• (0, -5) or (0, -1)

• (0, 5) or (0, 1)

Multiple Choice

The x-intercepts of a quadratic equation are known as the _____.

• vertices
• squares
• zeros
• formulas

Multiple Choice

Find the zero(s) of the function.

• x = 1

• x = -3

• x = {-1, 3}

• x = 2

Multiple Choice

Find the roots/zeros of x² + x - 2

• -1, 2

• -2, 1

Multiple Choice

Solve by factoring: x² + 3x - 18 = 0

• x = -3 and x = 6

• x = 3 and x = -6

• x = -9 and x = 2

• x = 9 and x = -2