Questions: Consider the following function. q(x) = -x^2 + 8x - 15 Find two points on the graph of the parabola other than the vertex and x-intercepts.

Transcript text: Consider the following function. \[ q(x)=-x^{2}+8 x-15 \] Step 3 of 4 : Find two points on the graph of the parabola other than the vertex and $x$-intercepts.

Solution

Solution Steps

Step 1: Define the Function

The function given is

\[ q(x) = -x^2 + 8x - 15 \]

Step 2: Select x-values

To find additional points on the graph of the parabola, we select $ x = 1 $ and $ x = 3 $, which are not the vertex or the x-intercepts.

Step 3: Calculate Corresponding y-values

Now, we calculate the corresponding $ y $-values for the selected $ x $-values:

For $ x = 1 $: \[ q(1) = -1^2 + 8 \cdot 1 - 15 = -1 + 8 - 15 = -8 \] Thus, the point is $ (1, -8) $.
For $ x = 3 $: \[ q(3) = -3^2 + 8 \cdot 3 - 15 = -9 + 24 - 15 = 0 \] Thus, the point is $ (3, 0) $.