Post on 08-Jan-2018
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THE QUADRATIC FORMULA§5.8
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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!
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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.
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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