10.4: Solving Quadratic Equations
Objective- To solve quadratic equations by graphing and by using square roots.
Investigate: Finding X-Intercepts
1. Find the X-Intercepts of each graph.
a.) y = 2x - 3
2. Solve for x: 2x – 3 = 0
b.) y = x 2 + 3x – 4
b.) Is the solution of 2x – 3 = 0 the same
as the X-Intercept?
3. Do the X-Intercepts that you graphed in 1b, satisfy the equation x 2 + 3x – 4 = 0?
4. Graph y = x 2 + x – 6.
b.) Find the X-Intercepts of the graph. Do they satisfy the
equation x 2 + x – 6 = 0?
Example 1: Solving by Graphing—Solve each equation by graphing the related function. How many
solutions will each have?
a.) 2x 2 = 0
b.) 2x 2 + 2 = 0
c.) 2x 2 – 2 = 0
Example 2: Find the solve each function by graphing. What are the roots?
a. x2 + 6x = -8
b. 2x2 + 2x + 2 = 0
Example 3: Real World Problem SolvingStudents perform an egg throw experiment in your math class. Assume both times he releases the
throw with the same initial speed but at different angles. The path of each throw can be modeled
by one of the equations below, where x represents the
horizontal distance in feet and y represents the vertical
distance in feet. Which angle results in a farther throw?