I have to find the vertex, axis of symmetry, and x intercepts of x^2-x+(5/4). I put it in standard form as -(x+-.5)^2+1.5. Thus, the vertex would be .5, 1.5. But the book's answer is 1/2, 1. How did they get this?

You got the standard form wrong.

x^2 - x + (5/4) = (x - 1/2)^2 + 1

The minimum (vertex) is at x = 1/2, and the value of y there is 1.

Where did the 1 come from in the standard form come from? How did the 5/4 become 1 when it was transferred to outside of the parentheses?

To find the vertex, axis of symmetry, and x-intercepts of the quadratic equation x^2 - x + (5/4), let's start by putting it in standard form as you did: -(x + a)^2 + b.

Compared to the given equation, we can see that a = -1/2 and b = 5/4.

To find the vertex, we need to determine the values of x and y which correspond to the maximum or minimum point of the quadratic function. In this case, since the coefficient of x^2 is positive, the parabola will have a minimum and the vertex will lie at the lowest point.

Using the formula for the x-coordinate of the vertex, which is given by x = -a, we have:
x = -(-1/2) = 1/2

Now, to determine the y-coordinate of the vertex, we substitute the x-value into the equation:
y = -(1/2 + (-1/2))^2 + 5/4
y = -(0)^2 + 5/4
y = 5/4

So, the vertex is (1/2, 5/4).

The axis of symmetry is a vertical line that passes through the vertex. Since the vertex has an x-coordinate of 1/2, the equation of the axis of symmetry is x = 1/2.

To find the x-intercepts, which are the values of x where the graph of the equation crosses the x-axis, we set y = 0 and solve for x:
-(x + (-1/2))^2 + 5/4 = 0
-(x - 1/2)^2 = -5/4

Now, we can solve for x by taking the square root of both sides and considering both the positive and negative roots:
x - 1/2 = ±√(5/4)
x - 1/2 = ±√5/2

Adding 1/2 to both sides, we obtain two solutions for x:
x = 1/2 ± √5/2

Therefore, the x-intercepts are (1/2 + √5/2, 0) and (1/2 - √5/2, 0).

The discrepancy between your calculated vertex of (0.5, 1.5) and the book's answer of (0.5, 1) seems to lie in the calculation of the y-coordinate of the vertex. It appears that a computation error may have occurred when substituting the x-value into the equation. Double-checking the calculation steps should help identify and resolve the issue.