Write function in vertex form?
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Please tell us what the vertex form is.
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Deleted member 4993
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I'm honestly not sure how to do these, that's all the book says.
"Write each function in vertex form" then it gives the problem..
You did not answer the question:
What is vertex form?
If your text-book does not have it - do a google search.
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Vertex form is:
\(\displaystyle y=a(x-h)^2+k\) where the point \(\displaystyle (h,k)\) is the vertex and \(\displaystyle a\ne0\) is a constant.
Suppose we are given a quadratic in standard form:
\(\displaystyle y=ax^2+bx+c\)
and we wish to write it in vertex form. This will involve completing the square on the RHS.
\(\displaystyle y=a\left(x^2+\dfrac{b}{a}x \right)+c\)
\(\displaystyle y=a\left(x^2+\dfrac{b}{a}x+\dfrac{b^2}{4a^2} \right)+c-a\left(\dfrac{b^2}{4a^2} \right)\)
\(\displaystyle y=a\left(x+\dfrac{b}{2a} \right)^2+c-\dfrac{b^2}{4a}\)
\(\displaystyle y=a\left(x-\left(-\dfrac{b}{2a} \right) \right)^2+\dfrac{4ac-b^2}{4a}\)
See if you can use the same technique on the quadratics you have been given, and post your work and we can guide you if you get stuck or make any mistakes.
\(\displaystyle y=a(x-h)^2+k\) where the point \(\displaystyle (h,k)\) is the vertex and \(\displaystyle a\ne0\) is a constant.
Suppose we are given a quadratic in standard form:
\(\displaystyle y=ax^2+bx+c\)
and we wish to write it in vertex form. This will involve completing the square on the RHS.
\(\displaystyle y=a\left(x^2+\dfrac{b}{a}x \right)+c\)
\(\displaystyle y=a\left(x^2+\dfrac{b}{a}x+\dfrac{b^2}{4a^2} \right)+c-a\left(\dfrac{b^2}{4a^2} \right)\)
\(\displaystyle y=a\left(x+\dfrac{b}{2a} \right)^2+c-\dfrac{b^2}{4a}\)
\(\displaystyle y=a\left(x-\left(-\dfrac{b}{2a} \right) \right)^2+\dfrac{4ac-b^2}{4a}\)
See if you can use the same technique on the quadratics you have been given, and post your work and we can guide you if you get stuck or make any mistakes.