Question 160017: Please help me with this question.
Write a quadratic equation with the given roots. Write the equation in standard form.
-2, -5
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! Write a quadratic equation with the given roots. Write the equation in standard form.
-2, -5
.
If these are roots, then it must be that:
(x+2)(x+5) = 0
.
Now, simply expand with FOIL and simplify:
(x+2)(x+5) = 0
x^2+5x+2x+10 = 0
x^2+7x+10 = 0
.
Standard form is:
f(x) = a(x - h)^2 + k
.
Grouping:
(x^2+7x)+10 = 0
Completing the square:
(x^2+7x+12.25)+10-12.25 = 0
(x+3.5)(x+3.5) - 2.25 = 0
(x+3.5)^2 - 2.25 = 0
.
Therefore:
f(x) = (x+3.5)^2 - 2.25
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