Quadratic Equations

Solving with the Quadratic Form

Answer the questions and take your notes :)

we have a mix of questions and notes slides.

For our lesson today...

Multiple Choice

Does the equation open or or down? 
Y = -3x² +7x - 2

• up
• down

Multiple Select

What are the green dots called?

• roots

• vertex

• solutions

• x intercepts

The standard form of a quadratic equation is ax²+bx+c

What are the values for a, b and c in the following quadratic equation?

3x²+5x-1

Dropdown

Make a true statement about about Graph C

The discriminant is ​​ ​

Select answer

There will be ​ ​

Select answer

Multiple Choice

What is this formula?

• This is the speed of light formula.
• This is the quadratic formula.
• This is the zero product property.
• This is scary.

What is the Discriminant??

This is part of the quadratic formula that informs us how how many solutions the quadratic equation will have.

Why is it Important??

When solving using the quadratic formula, you will know how many solutions you should have.

-a positive answer = 2 real roots

-a zero answer = 1 real root

-a negative answer = no real roots

Multiple Choice

What form is this equation in?
 2x²+4x-3=0

• general form
• vertex form
• factored form
• none of these

Finding the Discriminant

​Bonus: you can watch this video for more

Multiple Choice

What is the name of the imaginary line that cuts a parabola in half and goes through the vertex?

• the middle
• axis of symmetry
• minimum
• standard form

Multiple Choice

If the graph of a quadratic does not intercept the x-axis at any point, then it has:

• 1 Real Solution
• 2 Real Solutions
• Half a Solution
• No Real Solution

Multiple Choice

$$b^2-4ac$$  is called the . . .

• Square root

• Quadratic formula

• X-intercepts

• Discriminant 

Dropdown

Make a true statement about about Graph B

The discriminant is ​​

Select answer

There will be ​ ​

Select answer

Multiple Choice

Use the graph to determine the solutions.

• -1 and -3

• 1 and -3

• 1 and 3

• -1 and 3

Multiple Choice

$$m^2-5m-14=0$$  

• x = 7 and -2

• x = 7 and 2

• x = -7 and -2

• x = -7 and 2

Multiple Choice

Solutions of a quadratic equation are also called

• roots

• x-intercepts

• zeros

• All of the above

Multiple Choice

If there are no real solutions, the discriminant is

• zero

• a postive number

• a negative number

• a perfect square

Multiple Choice

If there is one solution, the discriminant is . . .

• zero

• a postive number

• a negative number

• a perfect square

Multiple Choice

$$2x^2-36=x$$  

• $$x=\frac{-9}{2}and\ 4$$  

• $$x=\frac{9}{2}\ and\ -4$$  

• $$x=4\ and\ -4$$  

• No real solution

Multiple Choice

Solve using the quadratic formula :

x² - 7x + 12 = 0

• x = 3, -4

• x = -3, 4

• x = 3, 4

• x = -3, -4

Multiple Choice

If the discriminant is equal to -2, how many solutions are there?

• No Solutions

• 1 Solution

• 2 Solutions

• Infinite Solutions

Multiple Choice

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

• -10 & -4
• -4 & 10
• -8 & 4
• 8 & -4

Multiple Choice

Determine the values of
a, b, and c for
the quadratic equation: 
4x² – 8x = 3
*remember right side should =0

• a = 4, b = -8, c = 3
• a = 4, b =-8, c =-3
• a = 4, b = 8, c = 3
• a = 4, b = 8, c = -3

Multiple Choice

Identify a, b, and c in: x²−6x+14

• a=3,b=5,c=9

• a=1,b=-6,c=14

• a=1,b=-6,c=-14

• a=1,b=6,c=14

Multiple Choice

Solve the following equation using the quadratic formula:

$$3x^2+16x+5=0$$  

• $$x=\frac{1}{3},\ x=5$$  

• $$x=-\frac{1}{3},\ x=-5$$  

• $$x=-1,\ x=-15$$  

• $$x=1,\ x=15$$  

Multiple Choice

Determine the values of a, b, and c for the quadratic equation:

4x² – 8x = 3

• a = 4, b = -8, c = 3

• a = 4, b =-8, c =-3

• a = 4, b = 8, c = 3

• a = 4, b = 8, c = -3

Multiple Choice

In the equation
$$x^2+5x+7\ =0$$   match each leading coefficient with its correct letter 

• $$a=0,b=5,c=7$$  

• $$a=1,b=5,c=7$$  

• $$a=7,b=5,c=1$$  

• $$a=x^2,\ b\ =\ 5x,\ c\ =\ 7$$  

Multiple Choice

Solve the following equation using the quadratic formula: $$5x^2-6=13x$$  

• $$x=-2,\ x=-\frac{3}{5}$$  

• $$x=2,\ x=\frac{3}{5}$$  

• $$x=3,\ x=-\frac{2}{5}$$  

• undefined