Quadratic Linear Systems

How many solutions

for the system:

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!!!

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

The function f(t) = -5t²+20t + 60 models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground?

• 4 seconds

• -2 seconds

• 6 seconds

• 9 seconds

Your friend passes you the ball during a soccer game. The height off the ground is modeled by the equation

h = -4t² + 12t. How high did the soccer ball get?

• 1.5

• 3

• 5

• 9

• 15

Solve the system. How many solutions this system has?