Graph the parabola and give its vertex, axis of symmetry. $x$-intercepts, and $y$-intercept.
\[
y=x^{2}-7 x+10
\]

The vertex is $(3,5,-225)$
(Type an ordered pair)
The axis of symmetry is (Type an equation. Use integers or fractions for any numbers in the equation)

Step 1 ：The given equation is \(y = x^2 - 7x + 10\).

Step 2 ：The vertex of a parabola given by the equation \(y = ax^2 + bx + c\) is given by the point \((-\frac{b}{2a}, f(-\frac{b}{2a}))\).

Step 3 ：In this case, \(a = 1\), \(b = -7\), and \(c = 10\). So, the vertex is \((-\frac{-7}{2*1}, f(-\frac{-7}{2*1})) = (3.5, f(3.5))\).

Step 4 ：The axis of symmetry is the vertical line passing through the vertex, given by the equation \(x = -\frac{b}{2a}\). In this case, the axis of symmetry is \(x = 3.5\).

Step 5 ：The $x$-intercepts are the solutions to the equation \(x^2 - 7x + 10 = 0\).

Step 6 ：The $y$-intercept is the point \((0, c)\). In this case, the $y$-intercept is \((0, 10)\).

Step 7 ：Calculating the $y$-coordinate of the vertex and the $x$-intercepts, we find that the $y$-coordinate of the vertex is $-2.25$, and the $x$-intercepts are $2$ and $5$.

Step 8 ：So, the vertex is \((3.5, -2.25)\), the axis of symmetry is \(x = 3.5\), the $x$-intercepts are \((2, 0)\) and \((5, 0)\), and the $y$-intercept is \((0, 10)\).

Step 9 ：Final Answer: The vertex is \(\boxed{(3.5, -2.25)}\), the axis of symmetry is \(\boxed{x = 3.5}\), the $x$-intercepts are \(\boxed{(2, 0)}\) and \(\boxed{(5, 0)}\), and the $y$-intercept is \(\boxed{(0, 10)}\).