Question

graph the equation $y = x^2 - 8x + 7$ on the accompanying set of axes. you must plot 5 points including the roots and the vertex. using the graph, determine the vertex of the parabola.
click to plot points. click points to delete them.

Explanation:

Step1: Find roots (y=0)

Set $y=0$, solve $x^2-8x+7=0$.
Factor: $(x-1)(x-7)=0$
Roots: $x=1, x=7$ → Points $(1,0)$ and $(7,0)$

Step2: Find vertex x-coordinate

Use $x=-\frac{b}{2a}$ for $ax^2+bx+c$.
$a=1, b=-8$, so $x=-\frac{-8}{2(1)}=4$

Step3: Find vertex y-coordinate

Substitute $x=4$ into $y=x^2-8x+7$.
$y=4^2-8(4)+7=16-32+7=-9$ → Vertex $(4,-9)$

Step4: Find 2 additional points

Choose $x=0$: $y=0^2-8(0)+7=7$ → $(0,7)$
Choose $x=8$: $y=8^2-8(8)+7=64-64+7=7$ → $(8,7)$

Answer:

The vertex of the parabola is $\boldsymbol{(4, -9)}$
The 5 points to plot are: $(0,7)$, $(1,0)$, $(4,-9)$, $(7,0)$, $(8,7)$