NEXT SAT IN: — DAYS, — HOURS, — MINUTES, — SECONDS. DON'T MISS YOUR CHANCE! SUBSCRIBE HERE

Solve by Graphing

Quadratic Vertex on the SAT: Desmos Walkthrough

Graph the height as a parabola, add the horizontal line for the target height, and click where they cross to read the time.

This lesson solves by graphing: turn the equation into curves, then read intersections, vertices, or tangency straight off the Desmos graph.

Take this lesson interactively

A real SAT-style question

A quadratic function models a projectile's height, in meters, above the ground in terms of the time, in seconds, after it was launched. The model estimates that the projectile was launched from an initial height of 7 meters above the ground and reached a maximum height of 51.1 meters above the ground 3 seconds after the launch. How many seconds after the launch does the model estimate that the projectile will return to a height of 7 meters?

A

3

B

6

C

7

D

9

How to solve it in Desmos, step by step

The idea

Graph the projectile's height as a quadratic in vertex form, then graph the line for height 7 and click where they cross again.

  1. 1

    Step 1

    Type this vertex-form parabola. It uses the peak at time 3, height 51.1, with a as a slider you will set next.

    Type in Desmos

    y=a(x−3)2+51.1y=a\left(x-3\right)^{2}+51.1
  2. 2

    Step 2

    Type this to set the slider value. Now the curve passes through time 0, height 7, the launch point, so it matches the projectile's path.

    Type in Desmos

    a=−4.9a=-4.9
  3. 3

    Step 3

    Type this to draw the horizontal line at height 7.

    Type in Desmos

    y=7y=7
  4. 4

    Step 4

    Click the right-hand gray dot where the parabola crosses the line. It reads time 6, height 7, so the projectile returns to 7 meters at 6 seconds. The answer is B.

The answer is B.

6

Now you try one

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

A quadratic function models a projectile's height, in meters, above the ground in terms of the time, in seconds, after it was launched. The model estimates that the projectile was launched from an initial height of 55 meters above the ground and reached a maximum height of 83.483.4 meters above the ground 44 seconds after the launch. How many seconds after the launch does the model estimate that the projectile will return to a height of 55 meters?

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

Exponential Increase Factor on the SAT with DesmosGeometry Visualization on the SAT with DesmosEquations with Exactly One Solution on the SAT with DesmosPerpendicular Lines and Points on the SAT with DesmosMass from Density and Volume on the SAT with DesmosQuadratic Roots and Coefficients on the SAT with Desmos
The full Desmos SAT course (all 31 lessons)15 Desmos SAT tricks (quick reference)Digital SAT Math formula sheet