Grade 11 · Math · Algebra 2

11th grade Write a quadratic function from three points worksheet

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Write a quadratic function from three points

Grade 11 Math Worksheet - Challenge Me

NameDate

Circle the best answer, or write your answer on the line.

Read this first
Use the table
x 1 2 3
y 3 9 23
Esme plots three points of a design in the table. The rule is y = ax² + bx + c. What is a?
Jun records three points of a kite's path in the table. The path is y = ax² + bx + c. What is a?
Luz's skate ramp passes through the points in the table. The ramp is y = ax² + bx + c. What is a?
Noah's design passes through the points in the table. Type x² as x^2. Which rule ax² + bx + c fits all three?
Pia's kite path passes through the points in the table. Type x² as x^2. Which rule ax² + bx + c fits all three?
Zee's swing path passes through the points in the table. Type x² as x^2. Which rule ax² + bx + c fits all three?
Esme times a water rocket launched from the ground. Its height follows h = at² + bt + c. How high is it at 3 s?
Jun times a water rocket launched from a 1 m stand. Its height follows h = at² + bt + c. How high is it at 3 s?
Luz times a model rocket launched from a 3-foot pad. Its height follows h = at² + bt + c. How high is it at 3 s?
Milo times a model rocket launched from the ground. Its height follows h = at² + bt + c. How high is it at 3 s?

x	1	2	3
y	3	9	23

11th grade Write a quadratic function from three points worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Write a quadratic function from three points. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can turn a point into an equation in a, b and c.
I can find a, b and c from three rows of a table.
I can write y = ax² + bx + c through three points and use it to predict a new row.

Standard: F-BF.A.1a

Words to know

row: One input and its output, like the point (2, 7).

mirror rows: Two rows the same distance either side of the vertex, with equal outputs.

second difference: How much the steps between outputs change; for rows 1 apart it is 2a.

eliminate: Add or subtract two equations so one letter cancels.

Common mistakes

Your child matched a with x and b with x².

Your child doubled x instead of squaring it.

Your child made the square of a negative number negative.

What to say

Ask: in y = ax² + bx + c, which letter sits next to x²?

Ask: is 3² the same as 2 × 3?

Ask: what is (-3) × (-3)?

Questions parents ask

What is the most common mistake with write a quadratic function from three points?

Your child matched a with x and b with x².

How can I help my child with write a quadratic function from three points?

Ask: in y = ax² + bx + c, which letter sits next to x²?

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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