Quadratic Linear Systems

The first thing I put into Desmos to help me identify the transitions of quadratic and square root formulas is ____________________.

Answer explanation

The first thing I put into Desmos to help me identify the transitions of quadratic and square root formulas is ____________________.

The Parent Function

This will help you see the transformation(s)

How many points of intersection are there

between the graphs of y=(x^2) and y=-3?

• 0

• 1

• 3

• 4

Answer explanation

If you notice the blue line y=-3 and the red quadratic y=(x^2) do not cross so the point of intersection is none.

How many real solutions does this system have?

(x^2)+(y^2)=25

x+3y=15

Answer explanation

You need to find where the lines intercept each other.

2 solutions

Put in Desmos:

How many real solutions does this system have?

y=(x^2)-2

y=x-6

Answer explanation

If the lines aren't touching then there are no solutions, none, zero, 0!!!

How many points of intersection are there between the graphs of f(x)=(x^2)+4 and g(x)=6x-5?

Hint with systems put them in desmos

• 4

• 2

• 1

• 0

Answer explanation

Those lines intersect one time!

How many points of intersection are there between the graphs f(x)=(-x^2)+3 and g(x)=1

Use Desmos :)

• 4

• 2

• 1

• 0

Answer explanation

g(x)=1 intersected with f(x)=(-x^2)+3 twice give this system two solutions.

Solve the following systems for x and y:

y=(x^2)+12x+14

y-x=-4

• (-9,-9),(12,-6)

• (9,13),(2,-6)

• (-1,9),(2,4)

• (-9,-13),(-2,-6)

Answer explanation

1. Put it in Desmos

2. Find intersection, if any

3. Your ordered pair of the intersection(s) is your real solutions

solve the systems:

y= -(x^2)+1

y=2x+1

• (-2,-5),(0,1)

• (0,1),(-1,0)

• (0,1),(2,-3)

• (0,1),(-2,-3)

Answer explanation

Find those connecting points and you have your solutions

Solve the system:

y=x^2

y=2-x

Answer explanation

Looking for the intercepting points

The Quadratic and Linear Systems DO NOT intersect so there are _________ solutions.

Answer explanation

No solutions, none, zero