Question

For the function h(x)=1/2x^2-7x+7, write the function in vertex form. h(x)=

Answer 1

To convert the function h(x) = (1/2)x^2 - 7x + 7 to vertex form, we complete the square and get h(x) = (1/2)(x - 7)^2 - 35/2.

Step-by-step explanation:

To write the function h(x) = \frac{1}{2}x^2 - 7x + 7 in vertex form, we need to complete the square. The procedure is as follows:

1. Factor out the coefficient of the x^2 term from the x-terms:

h(x) = \frac{1}{2}(x^2 - 14x) + 7

1. Find the number that completes the square for the expression in the parentheses:
2. To complete the square, take half of the x coefficient (-14/2 = -7) and square it (49), then add and subtract it inside the parentheses.

h(x) = \frac{1}{2}(x^2 - 14x + 49 - 49) + 7

1. Rewrite the equation, combining the constant terms:
2. h(x) = \frac{1}{2}((x - 7)^2 - 49) + 7
3. h(x) = \frac{1}{2}(x - 7)^2 - \frac{1}{2} \times 49 + 7
4. h(x) = \frac{1}{2}(x - 7)^2 - \frac{49}{2} + 7
5. Finally, simplify the constants:
6. Since 7 is the same as \frac{14}{2}, subtracting \frac{49}{2} from \frac{14}{2} gives us -\frac{35}{2}.

h(x) = \frac{1}{2}(x - 7)^2 - \frac{35}{2}

So, the function h(x) in vertex form is h(x) = \frac{1}{2}(x - 7)^2 - \frac{35}{2}.