Quiz about Quadratic Equation from Vertex and a Point

Question 1

Write the vertex form of the equation that has the indicated vertex and passes through the given point.
Vertex (4,-1); point (2,3)

Accepted Answer

$$f\left(x\right)=\left(x-4\right)^2-1$$

Answer

$$f\left(x\right)=\left(x-4\right)^2$$

Answer

$$f\left(x\right)=\left(x+1\right)^2-4$$

Answer

$$f\left(x\right)=\left(x+2\right)^2+3$$

Question 2

Write the vertex form of the equation that has the indicated vertex and passes through the given point.
Vertex (-2,5); point (0,9)

Accepted Answer

$$f\left(x\right)=\left(x+2\right)^2+5$$

Answer

$$f\left(x\right)=\left(x+5\right)^2+2$$

Answer

$$f\left(x\right)=\left(x-5\right)^2$$

Answer

$$f\left(x\right)=\left(x+2\right)^2-5$$

Question 3

Write the vertex form of the equation that has the indicated vertex and passes through the given point.
Vertex (-2,-1); point (0,3)

Accepted Answer

$$f\left(x\right)=\left(x+2\right)^2-1$$

Answer

$$f\left(x\right)=-\left(x+1\right)^2+3$$

Answer

$$f\left(x\right)=-\left(x+5\right)^2+7$$

Answer

$$f\left(x\right)=\left(x-3\right)^2$$

Question 4

Find the quadratic function with vertex (2, 0) and passing through (1, 3).

Accepted Answer

y = 3x² - 12x + 12

Answer

y = 3x² + 12x - 12

Answer

y = - 3x² + 6x - 1

Answer

y = 3x² - 6x + 9

Question 5

Write the vertex form of the equation that has the indicated vertex and passes through the given point.
Vertex (1,-2); point (-1,14)

Accepted Answer

$$f\left(x\right)=4\left(x-1\right)^2-2$$

Answer

$$f\left(x\right)=-2\left(x-14\right)^2-1$$

Answer

$$f\left(x\right)=\left(x+14\right)^2$$

Answer

$$f\left(x\right)=\left(x+1\right)^2-2$$

Question 6

Write the vertex form of the equation that has the indicated vertex and passes through the given point.
Vertex (5,12); point (7,15)

Accepted Answer

$$f\left(x\right)=\frac{3}{4}\left(x-5\right)^2+12$$

Answer

$$f\left(x\right)=\left(x-12\right)^2+15$$

Answer

$$f\left(x\right)=\frac{1}{3}\left(x-7\right)^2+15$$

Answer

$$f\left(x\right)=\left(x-7\right)^2+5$$

Question 7

Write a quadratic equation given the x intercepts and one other point.

Step 2: Find a.

Now that you know that the factors are (x-6) and (x-8), you must find a. Plug the coordinates of the vertex (7, 1) in for x and y and solve for a.

y = a(x-6)(x-8)

What is the value of a?

Accepted Answer

a = -1

Answer

a = 1

Answer

a = 7

Answer

a = -7

Question 8

If the vertex of this graph is (2, -1), what is the axis of symmetry?

Accepted Answer

x = 2

Answer

x= -1

Answer

y = -1

Answer

x = -2

Question 9

Does the quadratic have a max/min vertex, and does the parabola open up/down?

Accepted Answer

max/ opens down

Answer

min/ opens up

Answer

max/ opens up

Answer

min/ opens down

Question 10

What is the name of this form:
y = a(x - h)² + k

Accepted Answer

vertex form

Answer

standard form

Answer

factored form

Answer

zero form

Question 11

Identify the vertex and whether the graph opens up or down.

Accepted Answer

(1, 4); opens down

Answer

(-1, 4); opens up

Answer

(-1, 4); opens down

Answer

(1, 4); opens up

Quadratic Equation from Vertex and a Point

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