THE QUADRATIC FORMULA§5.8

VIDEO TIME!

Quadratic ForumlaticQuadratic Cups SongQuad Solve

THE QUADRATIC FORMULA

A quadratic equation written in standard form ax2 + bx + c = 0 can be solved with the

Quadratic Formula.

EXAMPLE 1: USING THE QUADRATIC FORMULA

Step 1) Write in standard form.

Step 2) Find the values of a, b, and c.

Step 3) Use the Quadratic Formula.

Step 4) Simplify.

The Quadratic Formula!

EXAMPLE 2: USING THE QUADRATIC FORMULA

Step 1) Write in standard form.

Step 2) Find the values of a, b, and c.

Step 3) Use the Quadratic Formula.

Step 4) Simplify.

The Quadratic Formula!

.122 2 xxSolve

EXAMPLE 3: USING THE QUADRATIC FORMULA

Step 1) Write in standard form.

Step 2) Find the values of a, b, and c.

Step 3) Use the Quadratic Formula.

Step 4) Simplify.

The Quadratic Formula!

EXAMPLE 4: USING THE QUADRATIC FORMULA

Step 1) Write in standard form.

Step 2) Find the values of a, b, and c.

Step 3) Use the Quadratic Formula.

Step 4) Simplify.

The Quadratic Formula!

Now graph the related function,

USING THE DISCRIMINANTQuadratic equations can have real or complex solutions. You can determine the type and number of solutions by finding the discriminant.

The discriminant of a quadratic equation in the form ax2 + bx + c = 0 is the value of the expression b2 – 4ac.

Discriminant

USING THE DISCRIMINANTValue of the Discriminant Type and Number of

Solutions for ax2 + bx + c =0

Examples of Graphs of Related Functions

y = ax2 + bx + c

b2 – 4ac > 0 Two real solutions Two x-intercepts

b2 – 4ac = 0 One real solution One x-intercept

b2 – 4ac < 0 No real solutions No x-intercepts

Is this possible? If so, what are the possible

answers?

EXAMPLE 5: USING THE DISCRIMINANTDetermine the type and number of solutions.

01065

0965

0865

2

2

2

xxc

xxb

xxa

)

)

)

VOLLEYBALL

Suppose a player makes a dig that propels the ball to the setter with an upward velocity of 25 ft/s. The function h = -16t2 + 25t models the height h in feet of the ball at time t in seconds. Will the ball ever reach a height of 10 ft?

Step 1) Substitute 10 for h.

Step 2) Find the values of a, b, and c.

Step 3) Evaluate the discriminant. Will the ball ever reach a

height of 8 feet?

Step 1) Substitute 8 for h.

Step 2) Find the values of a, b, and c.

Step 3) Evaluate the discriminant.

EXIT TICKET PICK 1 FROM EACH BOX TO SOLVE