Grade 9 · Math · Algebra 1

9th grade Vertex form y = a(x - h)² + k: graph it and write it worksheet

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Vertex form y = a(x - h)^2 + k: graph it and write it

Grade 9 Math Worksheet - Challenge Me

NameDate

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

Milo has a swing's graph, y = 2(x - 3)² - 5. Rewrite it as y = 2x² + bx + c. Type b, then c, with a comma between.
Noah has a whale's jump graph, y = -(x + 2)² + 7 (very splashy). Rewrite it as y = -x² + bx + c. Type b, then c, with a comma between.
Ren has a fountain's graph, y = -2(x - 4)² + 9. Rewrite it as y = -2x² + bx + c. Type b, then c, with a comma between.
Tala graphs a toy rocket's path on a grid. Write it as y = a(x - h)² + k. What are a, h and k? Type them in that order, with commas.
Zee graphs a deep bowl on a grid. Write it as y = a(x - h)² + k. What are a, h and k? Type them in that order, with commas.
Bo graphs a tent roof on a grid. Write it as y = a(x - h)² + k. What are a, h and k? Type them in that order, with commas.
Esme graphs a swing seat path on a grid. Write it as y = a(x - h)² + k. What are a, h and k? Type them in that order, with commas.
8.
Jun has two graph tracings. How must the graph of y = (x - 1)² + 2 move to become the graph of y = (x - 4)² - 3?
- Left 3, down 5
- Right 4, down 3
- Right 3, down 5
9.
Kira moves a kite curve on a grid. How must the graph of y = (x + 2)² + 1 move to become the graph of y = (x - 3)² + 4?
- Left 5, up 3
- Right 5, up 3
- Right 3, up 4
10.
Milo slides a traced curve (the pencil needs sharpening). How must the graph of y = (x - 5)² move to become the graph of y = (x - 2)² - 6?
- Right 2, down 6
- Left 3, down 6
- Right 3, down 6

Vertex form: graph it and write it. Every version has 10 questions, and the answer key prints on the second page.

I can read the vertex of y = a(x - h)² + k and say how the graph of y = x² moved.
I can find a from the vertex and one more point.
I can rewrite vertex form as y = ax² + bx + c.

Standard: F-IF.C.7a, F-BF.B.3, F-BF.A.1a, F-IF.C.8a

vertex form: y = a(x - h)² + k, with vertex (h, k).

shift: A slide of the whole graph left, right, up or down.

stretch: Outputs times a: size above 1 is narrower, below 1 is wider.

flip: A negative a turns the graph upside down.

Your child used the sign shown in the bracket, so the graph went the wrong way.

Your child swapped the sideways move and the up-or-down move.

Your child multiplied by the front number before squaring the bracket.

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

Ask: which number is inside the bracket with x?

Ask: what gets squared, the bracket or the bracket times the front number?

What is the most common mistake with vertex form y = a(x - h)² + k: graph it and write it?

Your child used the sign shown in the bracket, so the graph went the wrong way.

How can I help my child with vertex form y = a(x - h)² + k: graph it and write it?

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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