STEM:
If you can rewrite a quadratic equation as a product of factors that equals zero, you
c...
Mathematics, 23.06.2021 05:20 ASTROBOY1
STEM:
If you can rewrite a quadratic equation as a product of factors that equals zero, you
can solve the equation. To solve equations in this manner, you must use all your
factoring skills.
Example:
What are the solutions of the equation x2β x = 20?
First rewrite the equation so that one side equals zero.
x2β x = 20
x2 β x β 20 = 20 β 20
x2 β x β 20 = 0
Subtract 20 from each side.
Simplify.
Now, factor to rewrite the equation as a product of factors equal to zero. Find two
integers whose product is β20 and whose sum is β1. The product of 4 and β5 is
β20, and the sum of 4 and β5 is β1.
x + 4 = 0
x + 4 β 4 = 0 β 4
x = β4
x2 β x β 20 = 0
(x + 4)(x β 5) = 0
or
or
or
x β 5 = 0
x β 5 +5 = 0 +5
x = 5
The solutions are β4 and 5.
These "solutions" tell us where our quadratic function passess through the x-axis (ie this tells us the "roots" aka "x -intercepts" aka "zeros" aka "solutions" aka "zeros" are)
Question:
In the graph provided in the example, what do the coordinates (-4,0) and (5,0) represent?
A
The y- intercept of the function (ie where the function passes through the y-axis)
B
The x-intercept of the function (ie where the function passes through the x-axis)
C
The vertex of the function
D
none of the above
E
the zeros of the quadratic function
F
the roots of the quadratic function
Answers: 2
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