Name:____________________________________________
Date:_______ Period:______
Linear/Quadratic Systems
Recall: Graphing a linear function
Example:
Graph the line: y = 2x – 3
In order to graph a line, in y = mx + b form:
Step 1: List the slope and y-intercept.
Slope: ___________________________
y-intercept: _______________________
Step 2: Graph the y-intercept.
Step 3: From the y-intercept, use the slope to plot the other points on the line. Make
sure to fill up the entire graph.
Step 4: Using a straight-edge connect all of the points together.
In order to graph a line, in point/slope form: y - y1 = m(x - x1)
Example:
1
Graph the line: 𝑦 − 4 = − 2 𝑥 + 2
Step 1: List the slope and point.
Slope: ___________________________
Point: _______________________
Step 2: Graph the point.
Step 3: From the point, use the slope to plot the other points on the line. Make
sure to fill up the entire graph.
Step 4: Using a straight-edge connect all of the points together.
To graph a parabola: y = x2 – 4x – 5
Step 1: Find the axis of symmetry using the equation: 𝑥 =
−𝑏
2𝑎
Step 2: Plug the quadratic equation in y= in your calculator. Then check your table. The
axis of symmetry should be in the middle of your table. Use 3 values less than & 3 values
greater than your axis of symmetry to fill in the table.
***If your axis of symmetry is a fraction, use the two numbers that it falls
between as your middle numbers. However, make sure to graph your axis of
symmetry on your graph.***
Step 3: Plot all of the points from your table on the graph. Connect the points using a
curve.
To graph a quadratic/linear system:
Example:
y = x2 - 4x - 2
y=x–2
Step 1: Graph the line.
Step 2: On the same set of axes, graph the parabola.
Step 3: Write down the points where the line and parabola intersect. Box them in, this is
your final answer.
What happens if a quadratic/linear system is a Part I question?
If a quadratic/linear system is a Part I question, all that we have to do is use our graphing
calculator to solve!
Let's take a look at the same example:
y = x2 - 4x - 2
y=x–2
***Copy Down the Calculator Steps***
1) Solve the following quadratic/linear system graphically.
y = -x2 + 2x + 4
x+y=4
2) Solve the following system of equations graphically.
y = (x – 2)2 + 4
4x + 2y = 14