Question
How would I write quadratic fx: 3x^2-18x+25 in vertex form? Please list steps.
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Answer to a math question How would I write quadratic fx: 3x^2-18x+25 in vertex form? Please list steps.
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1. Start with the quadratic function:
f(x) = 3x^2 - 18x + 25
2. Factor out the coefficient of the \(x^2\) term from the first two terms:
f(x) = 3(x^2 - 6x) + 25
3. Complete the square inside the parentheses:
- Take half of the linear term (coefficient of \(x\)), square it, and add/subtract that value inside the parentheses.
- The linear term is -6, so half of it is -3, and squaring it yields 9.
f(x) = 3(x^2 - 6x + 9 - 9) + 25
4. Rewrite the equation to reflect the perfect square trinomial and simplify:
The perfect square trinomial is \((x - 3)^2\), so:
f(x) = 3((x - 3)^2 - 9) + 25
5. Distribute the 3 and combine constants:
f(x) = 3(x - 3)^2 - 27 + 25
f(x) = 3(x - 3)^2 - 2
6. The vertex form of the quadratic function is:
f(x) = 3(x - 3)^2 - 2
7. Answer:f(x) = 3(x - 3)^2 - 2
In this form, the vertex (h, k) is (3, -2)
2. Factor out the coefficient of the \(x^2\) term from the first two terms:
3. Complete the square inside the parentheses:
- Take half of the linear term (coefficient of \(x\)), square it, and add/subtract that value inside the parentheses.
- The linear term is -6, so half of it is -3, and squaring it yields 9.
4. Rewrite the equation to reflect the perfect square trinomial and simplify:
The perfect square trinomial is \((x - 3)^2\), so:
5. Distribute the 3 and combine constants:
6. The vertex form of the quadratic function is:
7. Answer:
In this form, the vertex (h, k) is (3, -2)
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