Lynn Marecek; MaryAnne Anthony-Smith; Andrea Honeycutt Mathis; Jay Abramson; Sharon North; Amy Baldwin; Alyssa Howell

Activity

Use the graphing tool or technology outside the course. Identify the function that matches each graph. Make sure your graph goes through all three points shown!

1.

Identify the function of Graph A.

A parabola on a coordinate grid. The parabola passes through 3 points that are labeled: (negative 1, 1), (0, 0), and (1, 1). The x-axis scale is 1 and extends from negative 6 to 6. The y-axis scale is 1 and extends from negative 6 to 6.

Compare your answer:

$y = x^{2}$

2.

Identify the function of Graph B.

A parabola on a coordinate grid. The parabola passes through 3 points that are labeled: (negative 3, 0), (0, negative 9), and (3, 0). The x-axis scale is 1 and extends from negative 6 to 6. The y-axis scale is 1 and extends from negative 10 to 2.

Compare your answer:

$y = x^{2} - 9$ or $y = (x - 3) (x + 3)$

3.

Identify the function of Graph C.

A parabola on a coordinate grid. The parabola passes through 3 points that are labeled: (negative 2, 0), (0.5, negative 6.25), and (3, 0). The x-axis scale is 1 and extends from negative 6 to 6. The y-axis scale is 1 and extends from negative 10 to 2.

Compare your answer:

$y = (x + 2) (x - 3)$

4.

Identify the function of Graph D.

A parabola on a coordinate grid. The parabola passes through 3 points that are labeled: (negative 6, 0), (negative 3, negative 9), and (0, 0). The x-axis scale is 1 and extends from negative 9 to 4. The y-axis scale is 1 and extends from negative 10 to 2.

Compare your answer:

$y = x (x + 6)$

5.

Identify the function of Graph E.

A parabola on a coordinate grid. The parabola passes through 3 points that are labeled: (negative 2, 0), (0, 4), and (2, 0). The x-axis scale is 1 and extends from negative 6 to 6. The y-axis scale is 1 and extends from negative 6 to 6.

Compare your answer:

$y = - x^{2} + 4$ or $y = (- x + 2) (x + 2)$

6.

Identify the function of Graph F.

A parabola on a coordinate grid. The parabola passes through 3 points that are labeled: (0, 4), (2, 0), and (4, 4). The x-axis scale is 1 and extends from negative 4 to 8. The y-axis scale is 1 and extends from negative 6 to 6.

Compare your answer:

$y = (x - 2) (x - 2)$ or $y = x^{2} - 4 x + 4$

7.

Identify the function of Graph G.

A parabola on a coordinate grid. The parabola passes through 3 points that are labeled: (negative 1, 0), (0, 3), and (3, 0). The x-axis scale is 1 and extends from negative 4 to 8. The y-axis scale is 1 and extends from negative 6 to 6.

Compare your answer:

$y = (- x - 1) (x - 3)$

8.

Identify the function of Graph H.

A parabola on a coordinate grid. The parabola passes through 3 points that are labeled: (0, 5), (1, 0), and (5, 0). The x-axis scale is 1 and extends from negative 4 to 8. The y-axis scale is 1 and extends from negative 5 to 7.

Compare your answer:

$y = (x - 1) (x - 5)$

9.

Identify the function of Graph I.

A parabola on a coordinate grid. The parabola passes through 3 points that are labeled: (negative 1, 2), (0, 0), and (1, 2). The x-axis scale is 1 and extends from negative 6 to 6. The y-axis scale is 1 and extends from negative 4 to 8.

Compare your answer:

$y = 2 x^{2}$

10.

Identify the function of Graph J.

A parabola on a coordinate grid. The parabola passes through 3 points that are labeled: (negative 4, negative 4), (0, 0), and (4, negative 4). The x-axis scale is 1 and extends from negative 6 to 6. The y-axis scale is 1 and extends from negative 8 to 4.

Compare your answer:

$y = - 0.25 x^{2}$

Video: Writing Equations that Represent a Quadratic Graph

Watch the following video to learn more about writing equations that represent a quadratic graph.

Access multimedia content

Self Check

Which equation describes the graph below?

$GRAPH OF A PARABOLA THAT OPENS UPWARD WITH A $y$-intercepts OF NEGATIVE 12 AND $x$-intercepts OF NEGATIVE 4 AND 3.$

$f(x) = x(x + 3)$
$f(x) = x + 12$
$f(x) = (x - 3)(x + 4)$
$f(x) = (x + 3)(x - 4)$

Additional Resources

Writing Quadratic Equations from Graphs

Write an equation for the graph below:

A parabola on a coordinate grid. The parabola passes through 3 points that are labeled: (negative 2, 0), (1, negative 9), and (4, 0). The x-axis scale is 1 and extends from negative 10 to 10. The y-axis scale is 1 and extends from negative 15 to 10.

First, locate the $x$ -intercepts at $(- 2, 0)$ and $(4, 0)$ .

Next, write the factor for each $x$ -intercept.

The factors that result in the given zeros are $(x + 2)$ and $(x - 4)$ .

The equation for this quadratic function is $f (x) = (x + 2) (x - 4)$ .

Use graphing technology to check your answer.

Try it

Try It: Writing Quadratic Equations from Graphs

Write an equation for the graph below:

A parabola on a coordinate grid. The parabola passes through 3 points that are labeled: (negative 6, 0), (negative 2, negative 16), and (2, 0). The x-axis scale is 1 and extends from negative 15 to 15. The y-axis scale is 1 and extends from negative 20 to 7.5.

Here is how to write an equation for the function graphed:

First, identify the $x$ -intercepts: $x = - 6$ , $x = 2 .$
Next, write a factor for each zero:
$(x + 6)$ and $(x - 2)$

The function in factored form is $f (x) = (x + 6) (x - 2)$ .

7.13.3 Writing Equations that Represent a Graph

Activity

Video: Writing Equations that Represent a Quadratic Graph

Additional Resources

Writing Quadratic Equations from Graphs

Try It: Writing Quadratic Equations from Graphs