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Big Ideas Math Algebra 1, 2015
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Big Ideas Math Algebra 1, 2015 View details
5. Using Intercept Form
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Exercise 40 Page 456

Start by rewriting the quadratic function in intercept form.

Practice makes perfect

To draw the graph of the given function, we will follow four steps.

  1. Rewrite the quadratic function in intercept form.
  2. Identify and plot the x-intercepts.
  3. Find and plot the y-intercept.
  4. Draw the parabola through the points where the x-intercepts and y-intercept occur.

Let's go through these steps one at a time.

Rewrite the Function

We will start by rewriting the function in intercept form. To do so, we will factor the right-hand side of the given equation.
y=x^2-x-30
WriteDiff

Write as a difference

y=x^2+5x-6x-30
â–Ľ
Factor out x & - 6
FactorOut

Factor out x

y=x(x+5)-6x-30
FactorOut

Factor out - 6

y=x(x+5)-6(x+5)
FactorOut

Factor out (x+5)

y=(x+5)(x-6)

Identify and Plot the x-intercepts

Recall the intercept form of a quadratic function. y=a(x-p)(x-q) In this form, where a ≠ 0, the x-intercepts are p and q. Let's consider the intercept form of our function. y=(x+5)(x-6) ⇕ y= 1(x-( - 5))(x- 6) We can see that a= 1, p= - 5, and q= 6. Therefore, the x-intercepts occur at ( - 5,0) and ( 6,0).

Find and Plot Y-intercept

The y-intercept is the point (0,c), where c represents a constant. In order to find it we just need to substitute 0 for x in the given equation.
y=x^2-x-30
Substitute

x= 0

y= 0^2- 0 -30
CalcPow

Calculate power

y=0- 0 -30
AddSubTerms

Add and subtract terms

y=- 30
The y-coordinate of the y-intercept is - 30. Therefore, the y-intercept is the point (0,- 30).

Draw the Parabola

We know that a= 1 >0, so the parabola opens up. Finally, we can draw the graph through the previously found points.

Subchapter links expand_more
arrow_right Communicate Your Answer p.449
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arrow_right Monitoring Progress p.451-454
Monitoring Progress 1 (Page 451)
Monitoring Progress 2 (Page 451)
Monitoring Progress 3 (Page 451)
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arrow_right Exercises p.455-458
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Exercises 7 (Page 455)
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