Question

find the \\(x\\)- and \\(y\\)-intercepts of the graph. do not graph the equation.

\\y = x^2 - 13x + 40\\

\\(x\\)-intercept \\((x, y) = \left(\text{smaller } x\text{-value}\
ight)\\)

\\(x\\)-intercept \\((x, y) = \left(\text{larger } x\text{-value}\
ight)\\)

\\(y\\)-intercept \\((x, y) = \left(\quad\
ight)\\)

Explanation:

Identify the given equation

We are given the quadratic equation:

$$y = x^2 - 13x + 40$$

Find the x-intercepts

To find the \(x\)-intercepts, set \(y = 0\):

$$x^2 - 13x + 40 = 0$$

Factor the quadratic expression:

$$(x - 5)(x - 8) = 0$$

Solve for \(x\):

$$x = 5 \quad \text{or} \quad x = 8$$

The smaller \(x\)-value gives the point \((5, 0)\).
The larger \(x\)-value gives the point \((8, 0)\).

Find the y-intercept

To find the \(y\)-intercept, set \(x = 0\):

$$y = 0^2 - 13(0) + 40$$

$$y = 40$$

The \(y\)-intercept is the point \((0, 40)\).

Answer:

Find the \(x\)- and \(y\)-intercepts of the graph. Do not graph the equation.

$$y = x^2 - 13x + 40$$

\(x\)-intercept \((x, y) =\) <blank>\((5, 0)\)</blank> (smaller \(x\)-value)
\(x\)-intercept \((x, y) =\) <blank>\((8, 0)\)</blank> (larger \(x\)-value)
\(y\)-intercept \((x, y) =\) <blank>\((0, 40)\)</blank>