VERTEX VAULT

Case File: Quadratic Equations

Agent Name:

Date:

MISSION OBJECTIVE

Determine the correct equation in vertex form \(y = a(x - h)^2 + k\) for each parabola described below. Use the given vertex and the additional point to solve for the lead coefficient \(a\).

01

Vertex: (0, 0); Point: (2, 4)

A) \(y = x^2\)

B) \(y = 2x^2\)

C) \(y = \frac{1}{2}x^2\)

D) \(y = 4x^2\)

02

Vertex: (1, 2); Point: (2, 5)

A) \(y = (x - 1)^2 + 2\)

B) \(y = 3(x - 1)^2 + 2\)

C) \(y = 3(x + 1)^2 + 2\)

D) \(y = (x + 1)^2 + 2\)

03

Vertex: (-2, 3); Point: (0, -1)

A) \(y = -2(x - 2)^2 + 3\)

B) \(y = -(x - 2)^2 + 3\)

C) \(y = -(x + 2)^2 + 3\)

D) \(y = -1(x - 2)^2 + 3\)

04

Vertex: (3, -4); Point: (5, 0)

A) \(y = 2(x - 3)^2 - 4\)

B) \(y = -1(x - 3)^2 - 4\)

C) \(y = \frac{1}{2}(x - 3)^2 - 4\)

D) \(y = (x - 3)^2 - 4\)

05

Vertex: (0, 5); Point: (1, 2)

A) \(y = -3x^2 + 5\)

B) \(y = 3x^2 + 5\)

C) \(y = -x^2 + 5\)

D) \(y = 7x^2 + 5\)

06

Vertex: (-1, -1); Point: (1, 7)

A) \(y = (x + 1)^2 - 1\)

B) \(y = 2(x + 1)^2 - 1\)

C) \(y = 2(x - 1)^2 - 1\)

D) \(y = 4(x + 1)^2 - 1\)

07

Vertex: (4, 2); Point: (2, -6)

A) \(y = -4(x - 4)^2 + 2\)

B) \(y = -2(x - 4)^2 + 2\)

C) \(y = 2(x - 4)^2 + 2\)

D) \(y = -2(x + 4)^2 + 2\)

08

Vertex: (-3, 0); Point: (-1, 8)

A) \(y = (x + 3)^2\)

B) \(y = 4(x + 3)^2\)

C) \(y = 2(x + 3)^2\)

D) \(y = 2(x - 3)^2\)

09

Vertex: (2, -2); Point: (3, -1)

A) \(y = 2(x - 2)^2 - 2\)

B) \(y = -(x - 2)^2 - 2\)

C) \(y = (x + 2)^2 - 2\)

D) \(y = (x - 2)^2 - 2\)

10

Vertex: (-5, -10); Point: (-3, 2)

A) \(y = 3(x + 5)^2 - 10\)

B) \(y = (x + 5)^2 - 10\)

C) \(y = -3(x + 5)^2 - 10\)

D) \(y = 6(x + 5)^2 - 10\)

11

Vertex: (1, 1); Point: (3, 9)

A) \(y = (x - 1)^2 + 1\)

B) \(y = 2(x - 1)^2 + 1\)

C) \(y = 4(x - 1)^2 + 1\)

D) \(y = -2(x - 1)^2 + 1\)

12

Vertex: (6, -3); Point: (4, 1)

A) \(y = (x - 6)^2 - 3\)

B) \(y = -(x - 6)^2 - 3\)

C) \(y = -2(x - 6)^2 - 3\)

D) \(y = 2(x - 6)^2 - 3\)

13

Vertex: (0, -4); Point: (2, -2)

A) \(y = x^2 - 4\)

B) \(y = \frac{1}{2}x^2 - 4\)

C) \(y = 2x^2 - 4\)

D) \(y = -\frac{1}{2}x^2 - 4\)

14

Vertex: (-4, 6); Point: (-2, -2)

A) \(y = -(x + 4)^2 + 6\)

B) \(y = -4(x + 4)^2 + 6\)

C) \(y = 2(x + 4)^2 + 6\)

D) \(y = -2(x + 4)^2 + 6\)

15

Vertex: (3, 3); Point: (0, 0)

A) \(y = -3(x - 3)^2 + 3\)

B) \(y = -(x - 3)^2 + 3\)

C) \(y = \frac{1}{3}(x - 3)^2 + 3\)

D) \(y = -\frac{1}{3}(x - 3)^2 + 3\)

16

Vertex: (-1, 5); Point: (0, 3)

A) \(y = 2(x + 1)^2 + 5\)

B) \(y = -2(x - 1)^2 + 5\)

C) \(y = -2(x + 1)^2 + 5\)

D) \(y = -(x + 1)^2 + 5\)

17

Vertex: (5, -1); Point: (7, 7)

A) \(y = (x - 5)^2 - 1\)

B) \(y = 4(x - 5)^2 - 1\)

C) \(y = -2(x - 5)^2 - 1\)

D) \(y = 2(x - 5)^2 - 1\)

18

Vertex: (-2, -2); Point: (-1, 0)

A) \(y = (x + 2)^2 - 2\)

B) \(y = 2(x - 2)^2 - 2\)

C) \(y = 4(x + 2)^2 - 2\)

D) \(y = 2(x + 2)^2 - 2\)

19

Vertex: (4, 0); Point: (6, 12)

A) \(y = 2(x - 4)^2\)

B) \(y = 3(x - 4)^2\)

C) \(y = 4(x - 4)^2\)

D) \(y = 3(x + 4)^2\)

20

Vertex: (-3, 4); Point: (-1, -4)

A) \(y = -1(x + 3)^2 + 4\)

B) \(y = -4(x + 3)^2 + 4\)

C) \(y = 2(x + 3)^2 + 4\)

D) \(y = -2(x + 3)^2 + 4\)

21

Vertex: (1, -5); Point: (0, -2)

A) \(y = 3(x + 1)^2 - 5\)

B) \(y = (x - 1)^2 - 5\)

C) \(y = -3(x - 1)^2 - 5\)

D) \(y = 3(x - 1)^2 - 5\)

22

Vertex: (-2, 2); Point: (0, -6)

A) \(y = 2(x + 2)^2 + 2\)

B) \(y = -2(x - 2)^2 + 2\)

C) \(y = -2(x + 2)^2 + 2\)

D) \(y = -(x + 2)^2 + 2\)

23

Vertex: (7, 1); Point: (8, 0)

A) \(y = (x - 7)^2 + 1\)

B) \(y = -2(x - 7)^2 + 1\)

C) \(y = -(x + 7)^2 + 1\)

D) \(y = -(x - 7)^2 + 1\)

24

Vertex: (0, 10); Point: (5, 0)

A) \(y = -2x^2 + 10\)

B) \(y = \frac{2}{5}x^2 + 10\)

C) \(y = -\frac{1}{2}x^2 + 10\)

D) \(y = -\frac{2}{5}x^2 + 10\)

25

Vertex: (-1, -1); Point: (-2, -3)

A) \(y = 2(x + 1)^2 - 1\)

B) \(y = -2(x - 1)^2 - 1\)

C) \(y = -2(x + 1)^2 - 1\)

D) \(y = -(x + 1)^2 - 1\)

26

Vertex: (3, -2); Point: (1, 6)

A) \(y = (x - 3)^2 - 2\)

B) \(y = 2(x - 3)^2 - 2\)

C) \(y = -2(x - 3)^2 - 2\)

D) \(y = 4(x - 3)^2 - 2\)

27

Vertex: (2, 5); Point: (4, 1)

A) \(y = -2(x - 2)^2 + 5\)

B) \(y = (x - 2)^2 + 5\)

C) \(y = -(x - 2)^2 + 5\)

D) \(y = -(x + 2)^2 + 5\)

28

Vertex: (-6, 0); Point: (-4, -4)

A) \(y = -(x - 6)^2\)

B) \(y = -1(x + 6)^2\)

C) \(y = -2(x + 6)^2\)

D) \(y = (x + 6)^2\)

29

Vertex: (1, 1); Point: (2, 4)

A) \(y = (x - 1)^2 + 1\)

B) \(y = 2(x - 1)^2 + 1\)

C) \(y = 3(x + 1)^2 + 1\)

D) \(y = 3(x - 1)^2 + 1\)

30

Vertex: (-2, -3); Point: (0, 5)

A) \(y = (x + 2)^2 - 3\)

B) \(y = 2(x - 2)^2 - 3\)

C) \(y = 4(x + 2)^2 - 3\)

D) \(y = 2(x + 2)^2 - 3\)

Mission Complete? Check your work against the known variables.

Vertex Vault Worksheet

Vertex Vault Worksheet

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