Question
find the vertex form of f(x)=2x^2+24x+70
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Answer to a math question find the vertex form of f(x)=2x^2+24x+70
Birdie
4.5103 Answers
1. Start with the given function:
f(x) = 2x^2 + 24x + 70
2. Factor out the coefficient of \(x^2\) from the first two terms:
f(x) = 2(x^2 + 12x) + 70
3. To complete the square, take the coefficient of \(x\), divide it by 2, and square it:
(12 / 2)^2 = 36
4. Add and subtract this square inside the brackets:
f(x) = 2(x^2 + 12x + 36 - 36) + 70
5. Group the perfect square trinomial and simplify:
f(x) = 2((x + 6)^2 - 36) + 70
6. Distribute the 2 and combine constants:
f(x) = 2(x + 6)^2 - 72 + 70
f(x) = 2(x + 6)^2 - 2
So the vertex form is:
f(x) = 2(x+6)^2 - 2
2. Factor out the coefficient of \(x^2\) from the first two terms:
3. To complete the square, take the coefficient of \(x\), divide it by 2, and square it:
4. Add and subtract this square inside the brackets:
5. Group the perfect square trinomial and simplify:
6. Distribute the 2 and combine constants:
So the vertex form is:
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