Quadratic Review

M1 Quadratic Review

Concepts and preparation for Quiz/Test

What did we practice yesterday with Quadratic f(x) ?

Using "technology" to find important features of Parabolas. We typed the Quadratic functions into the www.desmos.com calculator and simply analyzed the graphs for the points we needed.

Parabola with a Minimum

• 2 x-intercepts (aka roots, zeros)

• Note that the vertex IS the minimum

• It occurs at the bottom

• See that the axis of symmetry goes THROUGH the vertex

Parabola with a Maximum

• Axis of symmetry still goes THROUGH the vertex

• The vertex IS the maximum, at the top

• 2 x-intercepts (aka roots, zeros)

Multiple Choice

Standard form of a quadratic equation

• y=x²

• y=ax²+bx+c

• y=mx+b

• y=x

Multiple Choice

What is the equation for axis of symmetry?

• y=3

• x=3

• x=5

• x=1

Multiple Choice

What are the x-intercepts?

• 0 and 2

• -4 and 0

• 2 and 3

• 0 and 4

Multiple Choice

Use the graph to determine the roots:

• -1 and -3

• 1 and -3

• 1 and 3

• -1 and 3

Multiple Choice

What is another word for zeros?

• y-intercepts

• roots

• vertex

• axis of symmetry

Multiple Choice

Is this a max or min?

• max

• min

• cannot be determined

Multiple Choice

.How many zeros does this parabola have?

• 3

• 2

• 0

• 1

Multiple Choice

Does this graph have maximum or minimum value?

• maximum

• minimum

• neither

• both

How do we do this from the function?

• Use www.desmos.com to graph the function

• Simply click on the point(s) you are looking for

• Pay close attention to the coordinates!

Let's go to the graph!

• 2 x-intercepts: x = -2.118 and 0.118

• The vertex is a maximum, occurring at (-1, -5)

• The axis of symmetry equation would be x = -1

• The y-intercept is at (0, -1) --> always has an x-value of 0

One more example

Type the function into DESMOS and find the required points: zeros, vertex, and y-intercept

...and the winner is...

• The vertex is at (-5, 56); it is a maximum

• The x-intercepts are x = -10.292 and x = 0.292

• The y-intercept is at (0, 6)

Ok now it's your turn!

Make sure you have a www.desmos.com tab open and use it to answer the following questions:

Multiple Choice

Calculate the zeros of the quadratic.

• x = 6 and 3

• x = 1 and 0

• x = 0 and 3

• x = 3 and 1

Multiple Choice

Calculate the zeros of the quadratic.

• x = 2 and -3

• x = 0 and 9/4

• x = 0 and 4/9

• x = 1/2 and 1/3

Multiple Choice

What are the zeros of the function

f(x)= -4(x - 3)(x+5)?

• -12 and 20

• -5 and 3

• -4 and -5

• -3 and 5

Multiple Choice

Find the vertex.

y = -x² -10x + 3

• (5,-72)

• (28,-5)

• (-5, 78)

• (-5, 28)

Multiple Choice

Find the roots of y=5x²+7x-90

• (-5,0)(3.6,0)

• (0,-5)(0,3.6)

• (-4,0)(4,0)

• (-5,0)

Multiple Choice

What is the axis of symmetry of y=2x²-4x+9?

• x = 1

• x = -1

• x = -2

• x = 4

Multiple Choice

What is the vertex of y=x²+4x+3?

• (2,1)

• (-2,1)

• (0,0)

• (-2,-1)

Multiple Choice

What's the y-intercept of y = 3x²- 6x + 4

• (4,0)
• (-4,0)
• (0,-4)
• (0,4)

Multiple Choice

What's the axis of symmetry of y=3x²-6x+4

• x=1

• x=-6

• x=2

• x=-1