Quadratic Equations Preview

​Review the function graphs we have learned so far.

Take notes on the next slide's video

Multiple Choice

Standard form of a quadratic equation

• y=x²

• y=ax²+bx+c

• y=mx+b

• y=x

Multiple Choice

The graph of a quadratic function is called a

• Parabola

• Vertex

• Axis of Symmetry 

• Vertex Form

Multiple Choice

What is the equation for axis of symmetry?

• y = 3

• x = 3

• x = 5

• x = 1

Multiple Choice

The axis of symmetry line passes through which point?

• y-intercept

• any random point

• vertex

• symmetrical point for the vertex

Multiple Choice

A quadratic function is graphed on the grid.

Which answer choice best represents the domain and range of the function?

• Domain: $$x\ge-3$$  

  Range: $$y\ge5$$  

• Domain: All real numbers

  Range: $$y\ge5$$  

• Domain: $$x\ge-3$$  Range: All real numbers

• Domain: $$y\ge5$$  

  Range: $$x\ge-3$$  

Multiple Choice

What are the domain and range of the graph?

• Domain: all real numbers

  Range: $$y\ge5$$  

• Domain: all real numbers

  Range: $$y\le5$$  

• Domain: $$1\le x\le6$$  

  Range: $$y\ge-5$$  

• Domain: $$1\le x\le6$$  

  Range: $$y\le5$$  

Multiple Choice

A parabola is upside-down when the value of a is:

• negative

• positive

• 0

• infinite

Multiple Choice

What is the vertex?

• (2, 4)

• (3, -1)

• (0, 8)

• (4, 2)

Multiple Choice

What is the vertex?

• (5,2)

• (2,5)

• (-2,5)

• (-5,2)

Multiple Choice

Does this parabola have a minimum or maximum and what is its value?

• minimum: 2

• maximum: 2

• minimum: 5

• maximum: 5

Multiple Choice

Is this a maximum or a minimum?

• max

• min

• cannot be determined

Multiple Choice

What are the x-intercept(s) of this graph?

• -1 and -3

• -1 and 3

• 1 and 3

• 1 and -3

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 green dots called?

• axis of symmetry
• vertex
• parabola
• roots or x-intercepts

Multiple Choice

What are the x- intercepts?

• x= 0 and x= -4
• x= 0 and x= 4
• y= 0
• x= 2

Multiple Choice

Solve

x² + 2x - 20 = 4

• x = -6, x = 4

• x = 6, x = -4

• x = 12, x = -2

• x = 8, x = -3

Multiple Choice

Solve the following quadratic equation: $$4x^2-9=0$$  

• $$x=\frac{3}{2}$$  &  $$x=-\frac{3}{2}$$  

• $$x=\frac{2}{3}$$  & $$x=\frac{-2}{3}$$  

• $$x=\frac{9}{4}$$  

• $$x=\frac{4}{9}$$  

Multiple Choice

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

• { 2, 3 }
• { -2, -3 }
• { 2, 3 }
• { -2, 3 }

Explanation Slide...

​

Multiple Choice

What is the domain of the function?

• All Real Numbers

• -3 ≤ x ≤ 1

• y ≥ 4

• y ≤ 4

• -3≤ y ≥ 1

Explanation Slide...

​

Multiple Choice

What are the real roots (solutions) of the quadratic y = 2x²+4x+5

• (−1, 3)

• (0,5)

• (5,0)

• (3,-1)

• No real roots

Multiple Choice

Given a graph, how can you find the "solutions" to a quadratic?

• Call a friend

• Plug into a calculator

• Solutions are where the quadratic crosses the x-axis

• Magic 8 Ball -_-

Multiple Choice

Does this parabola have a maximum or minimum?

• Maximum
• Minimum

Multiple Choice

What is the parent function for all quadratics?

• Where the top of the graph is.

• Where it crosses the y-axis

• y=x²

• -4 and 0

Multiple Choice

What is the vertex of the quadratic?

• Where the top of the graph is.

• Where it crosses the y-axis

• y=x²

• -4 and 0

Multiple Choice

What are the solutions for the quadratic equation?

• Where the top of the graph is.

• Where it crosses the y-axis

• y=x²

• -4 and 0

Multiple Choice

What is general standard form of a quadratic?

• y=ax²+bx+c

• y=mx+b

• y=(x+h)(x+k)

• y=a(x+h)²+k

Multiple Choice

Given a graph, how can you find the "solutions" to a quadratic?

• Copy off neighbor

• Plug into calculator

• Solutions are where the quadratic crosses the x axis

• Magic 8 Ball

Multiple Choice

Which value is the vertex?

• (-4, 0)

• (-1, -9)

• (0, -8)

• (2, 0)