10.1 Graphing Quadratic Equations

10.1 Graphing Quadratic Equations

EQ: What are the two forms that we learned to graph? Write down the names, equations, and the important pieces of information needed

HW: Put it on your desk, I will walk around then put up the answers. NO WORK=NO CREDIT

A quadratic equation forms a parabola, a "U" shaped graph.

Multiple Choice

A parabola has a vertex at (-3,2).

Where is the axis of symmetry?

• y = -2

• x = 3

• y = 2

• x = -3

Multiple Choice

What is the axis of symmetry for the function

$$f\left(x\right)\ =\ 2x^2-20x-7$$  

We are going to put this one in your notes

• x= 5

• x=-5

• x= 20

• x=7/2

Multiple Choice

What is the green dashed line called?

• parabola

• roots or x-intercepts

• axis of symmetry

• line of dashes

Multiple Choice

Is the equation in standard form? If not, what should you do to get it in standard form?  $$2x^2\ -20x=7$$  

• Yes it is in standard form

• No, move the 20x to the other side

• No, move the 7 to the other side

• I don't know what standard form is.

Multiple Choice

What is the vertex of the function

$$y=-2x^2+4x+3$$  

• (0,3)

• (-1,5)

• (1,5)

• (1,-5)

Multiple Select

What are the x - intercepts of the quadratic shown? (Pick 2 answers)

• (2,0)

• (0,2)

• (0,6)

• (6,0)

​Write these steps down then take a break

Multiple Choice

What is the axis of symmetry for  $$2x^2-20x=7$$  

Hint: use  $$x=\frac{-b}{2a}$$  

• x=5

• x=-5

• x= 7/2

• x=20

Multiple Choice

This is what you should have found so far. Click on the image to enlarge. The next step is to pick 2 x’s close to the axis of symmetry and on the same side of the axis of symmetry. What would you pick? The axis of symmetry is x = 5

• 4 and 6

• 5 and 6

• 3 and 4

• 10 and 20

Poll

If you plug in 3 & 4 for x you’ll get the two points which are now graphed. When a graph has an axis of symmetry, it means the graph is the same on both sides. Do you see that you could reflect the new points across the axis of symmetry to get two more points on the other side? Click on image to make it larger.

• Yes

• No

Open Ended

Here’s what your graph should look like. What questions do you have?

Steps to graphing a quadratic equation in Vertex Form

• Identify the vertex (h,k)

• Select 2 more x's close to one side of the vertex to plug into the equation.

• Reflect those two points to the other side of the axis of symmetry

Multiple Select

Check all of the equations that are in standard form

• $$y=2x+1$$

• $$y=x^2+4x-9$$

• $$y=4\left(x-5\right)^2+3$$

• $$y=x^2+9$$

Multiple Select

Select all equations that are in vertex form

• $$y=x^2+5x$$

• $$y=3\left(x+4\right)^2-1$$

• $$y=-\left(x+3\right)^2-2$$

• $$y=\left(x+3\right)\left(x-2\right)$$

Multiple Choice

If given the equation y = 3(x + 5)² - 4, what is the vertex of the parabola?

• (5,-4)

• (-5,-4)

• (-15, 4)

• (15, -4)

Multiple Choice

Sketch the graph of the following function

HINT: Find the vertex and see which graph has the correct one

$$y\ =\ -\left(x-3\right)^2-3$$  

Multiple Choice

The axis of symmetry line passes through which point?

• y-intercept

• any random point

• vertex

​If the a is POSITIVE it opens UP

If the a is NEGATIVE it opens DOWN

Multiple Choice

What is the green dot on the parabola called?

• Root

• Zero

• Minimum

• Maximum

Multiple Choice

If given the equation

y = 3(x + 5)² - 4,

what is the vertex of the parabola?

• (-15, -4)

• (5, -4)

• (-5, -4)

• (15, -4)

Multiple Choice

Find the vertex. y = x²+ 16x + 71

• V(-8, 3)

• V(-8, 7)

• V(8, 10)

Multiple Choice

Given the equation for this parabola:

y=-(x-4)²-3,

does this parabola have a maximum or minimum value?

• Maximum

• Minimum

Multiple Choice

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

• (5, 2); opens up

• (-5, 2); opens up

• (5, 2); opens down

• (-5, 2); opens down

Application:

Open Ended

Make a prediction: What will be the maximum profit?

What is the maximum profit the company can expect to earn?

Multiple Choice

What are the zeros of the parabola? 

• 1, 5

• 3, -5 

• 3, 0

• -6, 1

Multiple Choice

What are the green dots called?

• axis of symmetry

• vertex

• parabola

• roots or x-intercepts

Multiple Choice

Determine the solutions of the graph:

• No Solutions

• (-3, 0) and (-1, 0)

• Infinity Many Solutions

• (-1, 0)

Multiple Choice

$$y=-2x^2+3x-7$$   This parabola opens...

• Upward

• Downward

Multiple Choice

$$y=-4x^2-2x+8$$   This parabola has a...

• Minimum

• Maximum

Homework:

Worksheet 4 problems