Writing Quadratic Equations

Writing Quadratic Equations

1. Identifying the vertex

2. Solving for a

3. Writing in vertex form

4. Changing to standard form

Multiple Choice

Whats the vertex of $$f\left(x\right)=\left(x-2\right)^2-5$$  

• (2,-5)

• (2,5)

• (-2,-5)

• (-2,5)

Multiple Choice

What is the vertex of $$f\left(x\right)=\left(x+4\right)^2$$  

• (0,4)

• (4,0)

• (-4,0)

• (0,-4)

Multiple Choice

What is the vertex of  $$f\left(x\right)=x^2-3$$  

• (0,3)

• (0,-3)

• (3,0)

• (-3,0)

Multiple Choice

Which of the following is the correct form for vertex form of a quadratic?

• $$x=a\left(y-h\right)^2+k$$  

• $$y=a\left(x-h\right)^2+k$$  

• $$y=a\left(x-k\right)^2+h$$  

• $$y=mx+b$$  

Multiple Choice

Identify the a, h, and k term from the following equation: $$\left(x+3\right)^2+2$$  

• a=-1, h=3, k=2

• a=3, h=3, k=3

• a=1, h=-3, k=2

• a=1, h=-3, k=-2

Multiple Choice

Identify the a, h, and k terms in the following equation: $$2\left(x+4\right)^2-1$$  

• a=2, h=-4, k=-1

• a=-2, h=4, k=1

• a=2, h=4, k=1

• a=-2, h=-4, k=1

Multiple Choice

Determine if the following equation has a maximum or minimum: $$-\left(x-2\right)^2+7$$  

• Maximum

• Minimum

Multiple Choice

Given the equation: y = -(x - 4)² - 3,

does this parabola have a maximum or minimum value?

• Maximum

• Minimum

Multiple Choice

Determine if the parabola has a maximum or minimum.

$$3\left(x+3\right)^2-2$$  

• Maximum

• Minimum

Match

Match the following:

Vertex $$\left(1,\ 6\right)$$ going through the point $$\left(-2,\ 0\right)$$

• h

• k

• x

• y

1

6

-2

0

• 1

• 6

• -2

• 0

Multiple Choice

Vertex $$\left(1,6\right)$$ going through point $$\left(-2,0\right)$$

Which of the following shows the values correctly substituted into the vertex form?

• $$0=a\left(-2-1\right)^2+6$$

• $$6=a\left(-2-1\right)^2+0$$

• $$0=a\left(1+2\right)^2+6$$

• $$6=a\left(1+2\right)^2+0$$

Multiple Choice

Vertex $$\left(1,6\right)$$ going through point $$\left(-2,0\right)$$ .

What is the value of a?

• $$3$$

• $$-\frac{2}{3}$$

• $$-\frac{3}{2}$$

• $$15$$

Math Response

Vertex $$\left(1,6\right)$$ going through point $$\left(-2,0\right)$$ .

What is the equation in standard form?

Use y= instead of f(x)=

Type answer here

Correct Answer: y=-\frac{2}{3}\left(x-1\right)^2+6

Deg^°

Rad