Grade 9 · Math · Algebra 1

9th grade Zeros of a quadratic, and writing one from its zeros or from a vertex and a point worksheet

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Zeros of a quadratic, and writing one from its zeros or from a vertex and a point

Grade 9 Math Worksheet - Challenge Me

NameDate

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

Zee's swing graph crosses the x-axis at -5 and -2 and passes through (-6, 16). Write it as y = ax² + bx + c. Write a, b and c, in that order, with commas.
Esme's rocket graph crosses the x-axis at -1 and 5 and passes through (3, 32). Write it as y = ax² + bx + c. Write a, b and c, in that order, with commas.
“The vertex is (2, 9)” Jun's table for a rainbow arc shows its vertex and two mirror rows. Write it as y = ax² + bx + c. Write a, b and c, in that order, with commas.
“The vertex is (1, -12)” Kira's table for a basketball shot shows its vertex and two mirror rows. Write it as y = ax² + bx + c. Write a, b and c, in that order, with commas.
“The vertex is (2, -9)” Luz's table for a bowl shows its vertex and two mirror rows. Write it as y = ax² + bx + c. Write a, b and c, in that order, with commas.
“The vertex is (-3, 12)” Milo's table for a ramp dip shows its vertex and two mirror rows. Write it as y = ax² + bx + c. Write a, b and c, in that order, with commas.
7.
Noah graphs a valley on a grid. Which equation makes this graph?
- y = -9(x + 2)(x - 4)
- y = (x + 2)(x - 4)
- y = -(x + 2)(x - 4)
- y = (x - 2)(x + 4)
8.
Pia graphs a deep bowl on a grid. Which equation makes this graph?
- y = 2(x - 1)(x - 5)
- y = 2(x + 1)(x + 5)
- y = (x - 1)(x - 5)
- y = -2(x - 1)(x - 5)
9.
Ren graphs a rainbow on a grid (it is a small rainbow). Which equation makes this graph?
- y = -(x + 3)(x - 1)
- y = -(x - 3)(x + 1)
- y = (x + 3)(x - 1)
- y = 4(x + 3)(x - 1)
10.
Tala graphs a tent roof on a grid. Which equation makes this graph?
- y = -x(x - 6)
- y = -2x(x - 6)
- y = 2x(x - 6)
- y = -2x(x + 6)

9th grade Zeros of a quadratic, and writing one from its zeros or from a vertex and a point worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Quadratics from their zeros or vertex. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can read the zeros and y-intercept of y = a(x - p)(x - q), and write the brackets for given zeros.
I can find the vertex halfway between the zeros, and find a from one more point.
I can write the quadratic in standard form from its zeros and a point, or from a vertex table.

Standard: A-APR.B.3, F-IF.C.8a, F-BF.A.1a

Words to know

zero: An input where the output is 0, an x-intercept.

factored form: y = a(x - p)(x - q), with zeros p and q.

standard form: y = ax² + bx + c.

bracket (factor): One of the parts multiplied, like (x - 3).

Common mistakes

Your child used the signs shown in the brackets, so the zeros came out with the wrong sign.

Your child gave where the graph crosses the y-axis instead of the x-axis.

Your child wrote the bracket for a negative zero as if the zero were positive.

What to say

Ask: what x makes (x - 3) equal 0?

Ask: on the x-axis, what is the output?

Ask: what x makes (x + 4) equal 0?

Questions parents ask

What is the most common mistake with zeros of a quadratic, and writing one from its zeros or from a vertex and a point?

Your child used the signs shown in the brackets, so the zeros came out with the wrong sign.

How can I help my child with zeros of a quadratic, and writing one from its zeros or from a vertex and a point?

Ask: what x makes (x - 3) equal 0?

Are these 9th 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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