Open solver

Solve SAT Math
with Desmos

Upload or type an SAT Math question. SolvePlot fills the calculator and explains the solution.

Solve a question
Sign in with Google or email
SolvePlot showing the uploaded quadratic question and explanation on the left, with Desmos data lists, a fitted parabola, and answer 143 on the right
A problem image is dragged into SolvePlot. After a brief loading indicator, SolvePlot displays the question and recommended regression method beside its automatically populated Desmos calculator. Data lists supply the points (1, 8), (2, 15), and (4, 35). The regression y₁ ~ ax₁² + bx₁ + c gives a = 1, b = 4, c = 3. Define f(x) = ax² + bx + c, then enter f(10) to get 143.

Solver

Upload or type a question. The calculator entries and their explanations appear together.

Interactive SolvePlot solution

Your problem

Replace
3x2−16x+2=0.3 x^{2} - 16 x + 2 = 0\text{.} One solution can be written as a+b6,\frac{a + \sqrt{b}}{6}\text{,} where a and bb are integers. What is a+b?a + b\text{?}

Your solution

Answer
248
Choice C

Bracket regression

Strategy

Use the graph’s two xx-intercepts to fit a and bb in the given root form.

In Desmos

Checking the Desmos lines…
Return to this method later
Answer choices
  • A
    6666
  • B
    132132
  • C
    248248
  • D
    296296
Question text

3x2−16x+2=0.3 x^{2} - 16 x + 2 = 0\text{.} One solution can be written as a+b6,\frac{a + \sqrt{b}}{6}\text{,} where a and bb are integers. What is a+b?a + b\text{?}

Calculator

Select a step to follow it on the graph

Loading calculator…

Loading calculator…
DemoOpen solver

AI Tutor

Choose Ask AI next to a line, or highlight the part you want explained.

Ask AI Tutor interactive example

In Desmos

3 lines
  1. 2TypeEnter line 2
    [(a+b)/6,(a−b)/6]∼[5.20526,0.128073][(a+\sqrt{b})/6,(a-\sqrt{b})/6]\sim[5.20526,0.128073]

    Match the plus form to the larger root and the minus form to the smaller root. The ~ sign asks Desmos to fit a and bb to those two values.

Fitting both unknowns

About calculator line 2

The ~ sign tells Desmos to find values of a and bb that make the two lists match. There are two unknowns, so both roots are needed.

Why it’s used here

Line 22 matches the plus form to 5.205265.20526 and the minus form to 0.128073.0.128073\text{.} Desmos fits a≈16a \approx 16 and b≈232b \approx 232 together.

Example

The fitted values shown by Desmos are:

a≈16,b≈232a\approx16,\quad b\approx232
DemoAsk about your question

History and Saved tricks

Your previous questions and the methods you’ve saved.

Saved tricks

History and Saved tricks interactive preview

Saved tricks

2 tricks saved

  • Bracket regression

    Graph the quadratic, then fit both root forms to the two xx-intercepts.

    Review trick · 3 lines

    One root of 3x2−16x+2=03 x^{2} - 16 x + 2 = 0 is (a + √bb) / 6,6\text{,} where a and bb are integers. Find a+b.a + b\text{.}

    1. y=3x2−16x+2y=3x^2-16x+2
    2. [(a+b)/6,(a−b)/6]∼[5.20526,0.128073][(a+\sqrt{b})/6,(a-\sqrt{b})/6]\sim[5.20526,0.128073]
    3. round⁡(a)+round⁡(b)\operatorname{round}(a)+\operatorname{round}(b)
    Answer 248248View solution

  • Three-point regression

    Fit a quadratic to the three given points, then evaluate the fitted function.

    Review trick · 5 lines

    A quadratic has f(1)=8,f \left(1\right) = 8\text{,} f(2)=15,f \left(2\right) = 15\text{,} and f(4)=35.f \left(4\right) = 35\text{.} Find f(10).f \left(10\right)\text{.}

    1. x1=[1,2,4]x_1=[1,2,4]
    2. y1=[8,15,35]y_1=[8,15,35]
    3. y1∼ax12+bx1+cy_1\sim ax_1^2+bx_1+c
    4. f(x)=ax2+bx+cf(x)=ax^2+bx+c
    5. f(10)f(10)
    Answer 143143

Planned features

Similar problems and practice by technique are in development.

Similar problems

Coming soon

Try another question that uses the same technique.

Your solutionAnswer 248
3x2−16x+2=03x^2-16x+2=0
Bracket regression
Similar problem1 / 2
2x2−9x+1=02x^2-9x+1=0

One root is (a+b)/4(a+\sqrt b)/4.
Find a + b.

Same technique

Practice by technique

Coming soon

Choose a technique to practice.

Your techniquesPractice
Question 1 of 3Fit a quadratic from a table
Preview

Frequently asked questions

View all questions
Do I need an account?

Yes. Sign in with Google or email to use the solver. Your solved questions are saved in History, and methods you save are available in Saved tricks.

How is the recommended method chosen?

SolvePlot looks for a short Desmos method using graphs, regressions, or lists. If a step needs work outside the calculator, the explanation tells you what to do.

Can I see another way to solve the same question?

Yes, when another checked method is available. Choose Other methods above the explanation to switch. Some questions also include an algebraic method.

Where do I change the theme and appearance?

Open Settings to choose a color palette, color amount, typography, button style, corner style, and light, dark, or system mode. The default is Candy with Colorful mode, Modern typography, Raised buttons, and Round corners. The calculator keeps its light appearance in every theme.

Try SolvePlot

Open solver