Section 2-7Solving Equations by Graphing

Essential Questions

• How do you find x- and y-intercepts of functions?

• How do you solve equations by examining graphs of the related functions?

Vocabulary1. Intercepts:

2. y-intercept:

3. x-intercept:

4. Root of the Equation:

5. Zero of a Function:

Vocabulary1. Intercepts: Points where a graph crosses an axis

2. y-intercept:

3. x-intercept:

4. Root of the Equation:

5. Zero of a Function:

Vocabulary1. Intercepts: Points where a graph crosses an axis

2. y-intercept: Point where a graph crosses the y-axis

3. x-intercept:

4. Root of the Equation:

5. Zero of a Function:

Vocabulary1. Intercepts: Points where a graph crosses an axis

2. y-intercept: Point where a graph crosses the y-axis

3. x-intercept: Point where a graph crosses the x-axis

4. Root of the Equation:

5. Zero of a Function:

Vocabulary1. Intercepts: Points where a graph crosses an axis

2. y-intercept: Point where a graph crosses the y-axis

3. x-intercept: Point where a graph crosses the x-axis

4. Root of the Equation: The solution to an equation

5. Zero of a Function:

Vocabulary1. Intercepts: Points where a graph crosses an axis

2. y-intercept: Point where a graph crosses the y-axis

3. x-intercept: Point where a graph crosses the x-axis

4. Root of the Equation: The solution to an equation

5. Zero of a Function: Another name for the root of the equation; The value of x for which f(x) = 0

Example 1Find the x- and y-intercepts of the graph.

y = 45x 2 + 12

5x − 8

Example 1Find the x- and y-intercepts of the graph.

y = 45x 2 + 12

5x − 8

x-intercepts:

Example 1Find the x- and y-intercepts of the graph.

y = 45x 2 + 12

5x − 8

x-intercepts:(-5, 0), (2, 0)

Example 1Find the x- and y-intercepts of the graph.

y = 45x 2 + 12

5x − 8

x-intercepts:

y-intercept:(-5, 0), (2, 0)

Example 1Find the x- and y-intercepts of the graph.

y = 45x 2 + 12

5x − 8

x-intercepts:

y-intercept:(-5, 0), (2, 0)

(0, -8)

Example 2Find the root of each equation by graphing the related

function.a. 0 = 1

3x + 2

Example 2Find the root of each equation by graphing the related

function.a. 0 = 1

3x + 2

x

y

Example 2Find the root of each equation by graphing the related

function.a. 0 = 1

3x + 2

x

y

Example 2Find the root of each equation by graphing the related

function.a. 0 = 1

3x + 2

x

y

Example 2Find the root of each equation by graphing the related

function.a. 0 = 1

3x + 2

x

y

Example 2Find the root of each equation by graphing the related

function.a. 0 = 1

3x + 2

x

y

Example 2Find the root of each equation by graphing the related

function.a. 0 = 1

3x + 2

x

y

Example 2Find the root of each equation by graphing the related

function.a. 0 = 1

3x + 2

x

y

Example 2Find the root of each equation by graphing the related

function.a. 0 = 1

3x + 2

x

y

Example 2Find the root of each equation by graphing the related

function.a. 0 = 1

3x + 2

x

y

Example 2Find the root of each equation by graphing the related

function.a. 0 = 1

3x + 2

x

y

The root is at x = -6

Example 2Find the root of each equation by graphing the related

function.a. 0 = 1

3x + 2

x

y

The root is at x = -6

The x-intercept is at (-6, 0)

Example 2Find the root of each equation by graphing the related

function.b. 0 = 5x −15

Example 2Find the root of each equation by graphing the related

function.b. 0 = 5x −15

xy

Example 2Find the root of each equation by graphing the related

function.b. 0 = 5x −15

xy

Example 2Find the root of each equation by graphing the related

function.b. 0 = 5x −15

xy

Example 2Find the root of each equation by graphing the related

function.b. 0 = 5x −15

xy

Example 2Find the root of each equation by graphing the related

function.b. 0 = 5x −15

xy

Example 2Find the root of each equation by graphing the related

function.b. 0 = 5x −15

xy

Example 2Find the root of each equation by graphing the related

function.b. 0 = 5x −15

xy

The root is at x = 3

Example 2Find the root of each equation by graphing the related

function.b. 0 = 5x −15

xy

The root is at x = 3

The x-intercept is at (3, 0)

Example 3Matt Mitarnowski found a service that allows him to download albums to his smart phone.

Each album costs $1.25 to download. He also paid a subscription fee of $8 to access or just stream the music. Someone needs to inform

him of Spotify Premium, where there is no extra fee on top of the subscription fee to sync music.

If the total cost for the download and subscription fee was $15.50, how many albums did he download? Solve by graphing the related

function.

Example 3

Example 3a = albums

Example 3

8 +1.25a = 15.50

a = albums

Example 3

8 +1.25a = 15.50

a = albums

−15.50−15.50

Example 3

8 +1.25a = 15.50

a = albums

−15.50−15.501.25a − 7.5 = 0

Example 3

8 +1.25a = 15.50

a = albums

−15.50−15.501.25a − 7.5 = 054a − 15

2= 0

Example 3

8 +1.25a = 15.50

a = albums

−15.50−15.501.25a − 7.5 = 054a − 15

2= 0

a

c

Example 3

8 +1.25a = 15.50

a = albums

−15.50−15.501.25a − 7.5 = 054a − 15

2= 0

a

c

Example 3

8 +1.25a = 15.50

a = albums

−15.50−15.501.25a − 7.5 = 054a − 15

2= 0

a

c

Example 3

8 +1.25a = 15.50

a = albums

−15.50−15.501.25a − 7.5 = 054a − 15

2= 0

a

c

Example 3

8 +1.25a = 15.50

a = albums

−15.50−15.501.25a − 7.5 = 054a − 15

2= 0

a

c

Example 3

8 +1.25a = 15.50

a = albums

−15.50−15.501.25a − 7.5 = 054a − 15

2= 0

a

c

Matt bought 6 albums