Solve by Element List Regression

Finding Quadratic Coefficient on the SAT: Desmos Walkthrough

Find where a parabola reaches its minimum or maximum by graphing the function in Desmos and clicking the vertex to read the

x

-value straight off the graph.

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

$f (x) = (x - 14) (x + 19)$

The function $f$ is defined by the given equation. For what value of $x$ does $f (x)$ reach its minimum?

$negative 266$

$negative 19$

$- \frac{33}{2}$

$- \frac{5}{2}$

How to solve it in Desmos, step by step

The idea

Graph the parabola and click its lowest point, the vertex. The x-value there is where f reaches its minimum.

1
Step 1
Type the function exactly as given. Desmos draws an upward parabola.
Type in Desmos
$y=\left(x-14\right)\left(x+19\right)$
2
Step 2
Find the lowest point of the curve and click the gray dot there. This is the vertex, which is the minimum.
3
Step 3
Read the coordinates Desmos shows. The vertex is at negative 5 over 2 comma negative 272.25, so the x-value at the minimum is negative 5 over 2. That matches choice D.

The answer is D.

$- \frac{5}{2}$

Now you try one

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

f(x) = (x - 23)(x + 11)

The function

f

is defined by the given equation. For what value of

x

does

f(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

More Desmos SAT lessons

Equivalent Expressions (Pt. 2) on the SAT with Desmos Circle Geometry with Perpendicular Bisector on the SAT with Desmos System of Linear Equations (No Solution) on the SAT with Desmos Reading a Coefficient off the Graph on the SAT with Desmos No-Real-Solution Quadratic on the SAT with Desmos Determining Coefficients of a Polynomial on the SAT with Desmos

The full Desmos SAT course (all 31 lessons)15 Desmos SAT tricks (quick reference)Digital SAT Math formula sheet