Solve by Element List Regression

Exponential Function Minimization on the SAT: Desmos Walkthrough

Graph the function directly and click the gray point at the bottom of the curve to read where its minimum happens.

This lesson uses sliders and direct evaluation in Desmos: put the unknown constant on a slider or a single expression line and let the calculator find the value instead of solving algebra by hand.

Take this lesson interactively

A real SAT-style question

$f (x) = 4 x^{2} + 64 x + 262$

The function $g$ is defined by $g (x) = f (x + 5)$ . For what value of $x$ does $g (x)$ reach its minimum?

$negative 13$

$negative 8$

$negative 5$

$negative 3$

How to solve it in Desmos, step by step

The idea

Graph g directly in Desmos and click the gray point at the bottom of the curve to read where the minimum happens.

1
Step 1
Type the original function. Desmos saves it so g can call it.
Type in Desmos
$f\left(x\right)=4x^{2}+64x+262$
2
Step 2
Type g as f of x plus 5. Desmos draws the shifted parabola.
Type in Desmos
$g\left(x\right)=f\left(x+5\right)$
3
Step 3
Click the gray dot at the lowest turning point of the g curve. Desmos shows the vertex as the point negative 13 comma 6, so the minimum happens at x equals negative 13. That is choice A.

The answer is A.

$negative 13$

Now you try one

Same question type, different numbers. Use the exact Desmos moves from the walkthrough above.

f(x) = 3x^2 + 42x + 190

The function

g

is defined by

g(x) = f(x + 4)

. For what value of

x

does

g(x)

reach its minimum?

Practice this with a live Desmos calculator

The interactive version of this lesson builds the Desmos graph up step by step as you click through, with a live calculator you can type into and your progress saved.

Open the interactive lesson

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