Linear-Quadratic Systems

Solving systems of linear quadratic equations

​Aim: SWBAT

• Solve systems of linear quadratic equations and use the quadratic formula

• Find the vertex and points on the graph

Vocab

Quadratic: Involving the second and no higher power of an unknown quantity

Linear: Extending along a straight and narrow line

Vertex: When two or more lines intersect

Linear Equations: Equations that graph as a line. They are equations that which the highest power of the variable is always 1.

Formulas

Linear: y=mx+b

Quadratic: y= ax²+bx+c

example Problem

​Solving graphically steps:

• Identify the linear and quadratic equation in the question. Use formula y= mx+ b for linear and y= ax² + bx + c

• Determine the vertex for the quadratic function

• Create a column where the left has the x-values, , middle has the y-values for the linear equation, and right value has the y-values for the quadratic equation

​You don't have to copy the steps!

Practice problem (Together)

​Find the solution using the quadratic formula

​Graph and plot the quadratics and find where they intersect. The points of intersection are the solutions.

​Copy this!

Multiple Choice

You try: Find the solution with the linear or quadratic formula

y= x² + 3x - 5

y = x +3

• (-4, -1) and (2, 5)
• (3, 2) and (5, 6)
• (0, 3) and (1, 4)
• (-2, 1) and (4, 5)

Multiple Choice

You try: Find the solution with the quadratic formula

y= x² - 4x+6

y= x+2

• (1 , 3) and (4, 6)

• (1 , 4)

• (-1, 1) and (4 , 2)

• (-1, 1) and (3, 6)

Multiple Choice

You try, fill in the blank: Always find the point where the quadratics

• Intersect
• Increase

• Decrease

• Pass

How many solutions does this system of equations have? Write this in your notebook

​Homework : )

​A) One
B) None
C) Two
D) All of the above

Homework : )

Find the different points on the graph