1. Lesson 9-4 Warm-Up

2. “Solving Quadratic Equations” (9-4)
What is a quadratic equation? What are the “roots of the equation” or the “zeros of the function”?
quadratic equation: a quadratic function (y = ax2 + bx + c) where y = 0 and written in the standard form: ax2 + bx + c = 0 Tip: Recall that to find the x-intercepts of a quadratic function, find x when y = 0. Therefore, the solution(s) of a quadratic equation are also the x-intercepts of the graph of the quadratic function (which is a parabola). Since a parabola can have two, one, or no points that cross the x-axis (x-intercepts), a quadratic equation can have two, one, or no solutions. The solutions of a quadratic equation and the related x-intercepts are called the roots of the equation or the zeros of the function.

3. “Solving Quadratic Equations” (9-4)
How do you solve a quadratic equation when b = 0?
To solve a quadratic equation, substitute 0 for y and solve for x. Example: y = x2 - 4 x2 - 4 = 0 Make y = 0 and write it in standard form (zero on right side of equal sign) Add 4 to both sides x2 = 4 Simplify x2 = 4 Find the square root of each side to eliminate the square (square root of a square is the number – the operations cancel each other out) x = 2 The square root of a number can be negative (-•- =+) The solutions, or x-intercepts, of y = x2 - 4 are 2 and -2.

4. Solve each equation by graphing the related function.
Solving Quadratic Equations
LESSON 9-4
Additional Examples
Solve each equation by graphing the related function.
a. 2x2 = 0
b. 2x2 + 2 = 0
c. 2x2 – 2 = 0
Graph y = 2x2
Graph y = 2x2 + 2
Graph y = 2x2 – 2
There is one solution, x = 0.
There is no solution.
There are two solutions, x = ±1.

5. x2 = 25 Square root both sides to isolate the x.
Solving Quadratic Equations
LESSON 9-4
Additional Examples
Solve 3x2 – 75 = 0.
3x2 – = Add 75 to each side.
3x2 = 75
x2 = 25 Divide each side by 3.
x2 = Square root both sides to isolate the x.
x = ± 5 Simplify.

6. “Solving Quadratic Equations” (9-4)
How can you solve a real world problem involving square roots?
To solve a real-world problem or equation involving square roots, negative solutions are not reasonable and thus should be eliminated (not used).

7. S = 4 r2, where S is the surface area and r is the radius.
Solving Quadratic Equations
LESSON 9-4
Additional Examples
A museum is planning an exhibit that will contain a large globe. The surface area of the globe will be 315 ft2. Find the radius of the sphere producing this surface area. Use the equation
S = 4 r2, where S is the surface area and r is the radius.
S = 4 r 2
315 = 4 r 2
Substitute 315 for S. 4 4
Divide each side by p (4).
315 4
= r 2
= r
315
(4)
Square root each side to isolate the r.  r
Use a calculator. Since a negative solution isn’t
reasonable (doesn’t make sense), only the positive
solution should be used.
The radius of the sphere is about 5 ft.

8. 2. Solve each equation by finding square roots. a. m2 – 25 = 0
Solving Quadratic Equations
LESSON 9-4
Lesson Quiz
1. Solve each equation by graphing the related function. If the equation has no solution, write no solution.
a. 2x2 – 8 = 0
b. x2 + 2 = –2
2. Solve each equation by finding square roots.
a. m2 – 25 = 0
b. 49q2 = 9
3. Find the speed of a 4-kg bowling ball with a kinetic energy of 160 joules. Use the equation E = ms2, where m is the object’s mass in kg, E is its kinetic energy, and s is the speed in meters per second. ±2
no solution ±5 3 7 1 2
about 8.94 m/s