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 - Building Confidence

NameDate

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

Ren graphs a valley on a hiking map, y = (x + 2)(x - 4). Where does the graph cross the x-axis? Type both x-values, smaller first, with a comma between.
Tala graphs a fruit bowl, y = (x + 5)(x + 2) (the grapes are not on the graph). Where does the graph cross the x-axis? Type both x-values, smaller first, with a comma between.
3.
Bo's kite-string graph crosses the x-axis at x = 2 and x = -4. Which equation has these zeros?
- y = (x - 4)(x - 2)
- y = (x + 4)(x - 2)
- y = (x - 4)(x + 2)
4.
Esme's rainbow graph crosses the x-axis at x = -1 and x = 5 (a double rainbow would need two graphs). Which equation has these zeros?
- y = (x - 1)(x - 5)
- y = (x + 1)(x - 5)
- y = (x - 1)(x + 5)
5.
Jun's swing graph crosses the x-axis at x = 3 and x = -6. Which equation has these zeros?
- y = (x + 6)(x - 3)
- y = (x - 6)(x - 3)
- y = (x - 6)(x + 3)
6.
Kira's boat-wake graph crosses the x-axis at x = -7 and x = 1. Which equation has these zeros?
- y = (x - 7)(x + 1)
- y = (x - 7)(x - 1)
- y = (x + 7)(x - 1)
Luz graphs a ball bounce, y = (x - 3)(x + 5). Where does the graph cross the y-axis? Give the y-value.
Milo graphs a mixing bowl, y = (x + 3)(x + 8). Where does the graph cross the y-axis? Give the y-value.
Noah graphs a dip in a bike path, y = 2(x + 1)(x - 4). Where does the graph cross the y-axis? Give the y-value.
Pia graphs a toy rocket arc, y = -3(x - 2)(x + 1) (three, two, one, graph!). Where does the graph cross the y-axis? Give the y-value.

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

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

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).

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.

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?

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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