1. THE QUADRATIC FORMULA

2. WHAT IS IT FOR? The quadratic formula is used to solve
quadratic equations.
What is a quadratic equation?
What does it mean to solve?
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3. QUADRATIC EQUATIONS
To use the quadratic formula the equations must be in descending order equal to zero (aka Standard Form).
All quadratic equations can be written in this form where: a, b, and c are constants and “a” cannot be zero.
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4. SHAPE OF A QUADRATIC
The shape of all quadratic functions (equations) is a parabola.
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5. OTHER EXAMPLES Here are some more examples of quadratic equations:
Notice in the last one that there is no c term.
This is not a mistake. Notice also that all quadratic
equations have a squared variable.
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6. QUADRATIC FUNCTIONS On the previous page, you noticed that
quadratic equations were written to equal zero.
This will be explained later.
They can also be written equal to ‘y’. This is called a quadratic
function.
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7. TO SOLVE QUADRATIC EQUATIONS
To solve a quadratic equation means to really find the
point where the parabola crosses the ‘x’ axis.
‘x’ axis is the horizontal line
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8. GRAPHING TO SOLVE evaluate the quadratic function
and record a table of values
Plot the points to find out where the parabola crosses the ‘x’ axis.
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9. ‘X’ AXIS CROSSING
Where does the parabola cross the ‘x’ axis?
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10. VALUE OF ‘Y’ AT ‘X’ AXIS
The parabola crosses the ‘x’ axis at -3 and -2.
Notice the value of the ‘y’ coordinate at these points. It is 0.
(-3,0) and (-2, 0)
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11. VALUE OF ‘Y’
Remember earlier we had the quadratic equations equal to zero. That just means that when we solve them, we are finding the ‘x’ value (the place the parabola crosses the ‘x’ axis) when the ‘y’ value is zero.
This looks very similar to the quadratic function below.
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12. USING THE QUADRATIC FORMULA TO SOLVE
Remember the quadratic formula shown earlier.
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13. QUADRATIC FORMULA We can use the quadratic formula
to solve (find the ‘x’ axis crossing point) of quadratic equations.
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14. QUADRATIC FORMULA
We have to remember the standard form of a quadratic equation.
The quadratic formula is really a rearranged version of the
standard form of a quadratic equation. It can be rearranged
to solve for x ( the place the parabola crosses the ‘x’ axis).
It could be rewritten to read as below.
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15. USING THE FORMULA Look at the quadratic equation below and compare
it to the standard form of a quadratic equation.
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16. USING THE FORMULA
Simply list your a, b, and c values from your quadratic
equation and plug them into the quadratic formula.
a=1 (if there is no number before x2, assume a = 1).
b=5
c=6
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17. USING THE FORMULA
a=1
b=5
c=6
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18. USING THE FORMULA a=1 b=5 c=6
Replace a, b, and c in the formula and look what you have.
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19. USING THE FORMULA
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20. USING THE FORMULA
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21. ANSWERS
CONGRATULATIONS! YOU DID IT! Try more examples on page 231 in the Math 11 textbook.
Since there is no ‘c’ value, use 0 for c.
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22. Your Turn

24. Your turn. What are the solutions to the quadratic x2 - 2x - 48 = 0?
a = 1 b = -2 c = -48
¡ A. 6 and 8
¡ B. -6 and -8
¡ C. -6 and 8
¡ D. 6 and -8
¡ E. 3 and 16

25. Quadratic Formula 0 = 2y2 + 4y - 1 a = 2 b = 4 c = -1
-4, 2, and 4 are all three divisible by two and therefore can be reduced.

26. D2. What are the solutions to the quadratic x2 - 2x - 48 = 0?
Set each factor to 0
x - 8 = 0
x = 8
x + 6 = 0
x = -6
x = { 8, -6}
¡ A. 6 and 8
¡ B. -6 and -8
¡ C. -6 and 8
¡ D. 6 and -8
¡ E. 3 and 16
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27. D10. What are the solutions to the quadratic x2 - 10x + 24 = 0?
¡ A. 4 and 6
¡ B. -4 and 6
¡ C. -4 and -6
¡ D. 2 and -12
¡ E. -2 and 12
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28. No Real Roots
Since there is no real number that is the square root of a negative number, this equation has no real roots.

29. THE QUADRATIC FORMULA