REVIEW QUADRATIC EQUATIONS

Quadratic Equations

Labeling

Label the key pieces of a quadratic graph.

Drag labels to their correct position on the image

Y-intercept

Vertex

X-Intercept

Quadrat

Zero

Roots

Let's recap this in Vertex Form

Let's begin by labeling important pieces of the equation!!!

What is the vertex coordiante point?

Is it a Maximum or Minimum?

Drag and Drop

Drag and drop the correct labels of the following equation: $$f\left(x\right)=3\left(x+6\right)^2-4$$ ​ ​

Placeholder

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Placeholder

Drag these tiles and drop them in the correct blank above

Minimum

(-6,-4)

(6,-4)

Maximum

Drag and Drop

Drag and drop the correct labels of the following equation: $$f\left(x\right)=-4\left(x-10\right)^2$$ ​ ​

Placeholder

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Placeholder

Drag these tiles and drop them in the correct blank above

Maximum

(10,0)

Minimum

(6,-4)

Multiple Select

What can the roots to a quadratic equation be called?

• zeros

• solutions

• x-intercepts

• none of the choices

Multiple Choice

What are the x- intercepts?

• x= 0 and x= -4

• x= 0 and x= 4

• y= 0

• x= 2

Multiple Choice

Solve the following quadratic equation: $$5x^2=10x$$  

• $$x=-2$$  

• $$x=2$$  

• $$x=2$$  & $$x=0$$  

• $$x=-2$$  & $$x=0$$  

Multiple Choice

Solve for the values of x:
(x + 2)(x - 3) = 0

• { 2, 3 }

• { -2, -3 }

• { 2, 3 }

• { -2, 3 }

Multiple Choice

Solve Using the Quadratic Formula
 x² + 4x - 40 = -8

• -10 & -4

• -4 & 10

• -8 & 4

• 8 & -4

Multiple Choice

What would this quadratic function look like?

$$y=-2x^{2\ }+3x\ +4$$  

​Let's take a look...

​What did we do previously if we wanted to find out the value of x, when y = 0, i.e.

​y = 0 , x = ?

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​Here's a question....

Multiple Choice

To find out the value of x, when y = 0, we had to:

• Draw the line, $$x\ =\ 0$$  

• Draw the line,  $$x\ =\ 2$$  

• Draw the line, $$y\ =\ 0$$  

• Draw the line,

  $$y=2$$  

​Yes, we drew the line

​This is a special case, because y = 0 is actually coincides with the x-axis.

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Therefore, these values of x are called the x - intercepts.

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Fill in the Blanks

What are the values of x when y = 0 for the quadratic function  $y=-2x^{2\ }+3x\ +4$  ? 

(Just type one answer to 3 decimal places)

​Now, let us review what we did...

​For the quadratic function,

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​When we wanted to find the x values, ( x = ? ) we drew the function,

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If we combined the two functions above, we get a quadratic equation.

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​Let's recap a bit more...

Whenever we have an equation, the two sides must equal. So for the quadratic equation,

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​what do you think would be the values of x that would make the equation true?

Have you guessed it?

​Yes, the values that we got just now...

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these are called the solutions or the roots ​make the equation below true.

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Try it out...

Multiple Choice

So now, if i wanted to find the roots for the quadratic equation,  $$-2x^2+3x+4\ =\ 3$$   what would you do?

• Reuse the function  $$y=-2x^2+3x+4$$  and draw the function  $$y=3$$  and find the intercepts.

• Panic!

Fill in the Blanks

So, the roots of the equation,  $-2x^2+3x+4\ =3$  is...

(just type one answer to 3 decimal places)

Multiple Choice

Convert the following quadratic equation to standard form.

$$4x^2+21x=-6$$  

• $$4x^2+21x-6=0$$  

• $$4x^2+21x+6=0$$  

Multiple Choice

What is the "c" term of the following quadratic equation:

$$2x^2+5x=0$$  

• -6

• 5

• 0

• 6

Multiple Choice

What is the first step when solving a quadratic equation by factoring?

• Put the equation in standard form

• Factor

• Set the factors equal to zero and solve.

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

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

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

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