Quadratic Linear System

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?

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 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 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

Using substitution, which of the following equations could be used to solve the system:
y = x² + 3x - 5
y = x + 3

• x² - 3x + 5 = x - 3

• x² + 3x - 5 = x + 3

• x² + 3x - 5 + x + 3 = 0

• x² + 3x - 5 = 0

Which of the following is NOT a possible number of solutions to a system containing one linear function and one quadratic function?

• 1

• 2

• 3

• 0

Which of the following points is a solution to the system:
y = x² + 4x + 2
y = x + 2

• (-3, -1)

• (-1, 2)

• (1, -2)

• (2, 4)

Which point is NOT a solution to this system of inequalities?

• (0,0)

• (-4,4)

• (-6,-1)

• (-2, 0)

Is the point (1, 6) in the solution set of
y < x² + 2x + 2? 
(hint: plug it in and test if it's a solution) 

• YES

• NO

Where is the AOS (Axis of Symmetry) for 
y = -2x²+4x+2

• x = 2

• x = 1

• x = -1

• x = 4