The graph of is shown. The function can be written in the form , where is a constant. Which choice is the value of ?

Solution available with step-by-step explanation

SAT Nonlinear Functions Question 92 | Free SAT Prep | Aniko

00:00

Question 92·Medium·Nonlinear Functions

0 / 234

The graph of $y=f(x)$ is shown.

The function can be written in the form $f(x)=a(x+1)(x-5)$ , where $a$ is a constant.

Which choice is the value of $a$ ?

When a function is given in factored form, use an easy-to-read point from the graph (often an intercept). Substitute that point into the expression to create a simple equation in the unknown constant, then solve, paying close attention to negative signs.

Hints

Click me!

Use the y-intercept

Look for the point where the graph crosses the y-axis. That point has $x=0$ .

Plug in $x=0$

Substitute $x=0$ into $f(x)=a(x+1)(x-5)$ and set it equal to the y-value you read from the graph.

Watch the signs

Compute $(0+1)(0-5)$ carefully before solving for $a$ .

Desmos Guide

Enter the factored function with a slider

Type $y=a(x+1)(x-5)$ and allow Desmos to create a slider for $a$ .

Match the y-intercept from the graph

Look at the graph’s y-intercept (where $x=0$ ), which is $(0,-10)$ . In Desmos, adjust the slider until the parabola’s y-intercept is $-10$ .

Read the slider value

When the y-intercept matches $(0,-10)$ , note the value of $a$ shown on the slider.

Step-by-step Explanation

Read a point from the graph

The graph shows the y-intercept at $(0,-10)$ , meaning $f(0)=-10$ .

Substitute into the given factored form

Use $f(x)=a(x+1)(x-5)$ with $x=0$ :

-10=a(0+1)(0-5)

-10=a(1)(-5)=-5a

Solve for $a$

Divide both sides by $-5$ :

a=2

So the correct choice is $2$ .

Strategy

Hints

Desmos Guide

Step-by-step Explanation

Study Hints

Strategy

Hints

Desmos Guide

Step-by-step Explanation