body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Big Ideas Math Algebra 1, 2015

BI

Big Ideas Math Algebra 1, 2015 View details

5. Using Intercept Form

Continue to next subchapter

Exercise 41 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.

Rewrite the quadratic function in intercept form.
Identify and plot the x-intercepts.
Find and plot the y-intercept.
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=- 5x^2-10x+40

Factor out - 5

y=- 5(x^2+2x-8)

Write as a sum

y=-5(x^2-2x+4x-8)

▼

Factor out x & 4

Factor out x

y=-5(x(x-2)+4x-8)

Factor out 4

y=-5(x(x-2)+4(x-2))

Factor out (x-2)

y=-5(x-2)(x+4)

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=- 5(x-2)(x+4) ⇕ y= -5(x- 2)(x-( - 4)) We can see that a= - 5, p= 2, and q= - 4. Therefore, the x-intercepts occur at ( 2,0) and ( - 4,0).

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=- 5x^2-10x+40

x= 0

y=- 5( 0)^2-10( 0)+40

Calculate power

y=5(0)-10(0) +40

Zero Property of Multiplication

y=0-0+40

Add and subtract terms

y=40

The y-coordinate of the y-intercept is 40. Therefore, the y-intercept is the point (0,40).

Draw the Parabola

We know that a= - 5 <0, so the parabola opens down. Finally, we can draw the graph through the previously found points.

Subchapter links

Communicate Your Answer p.449

Monitoring Progress p.451-454

Exercises p.455-458