Question

graph the equation $y = x^2 - 10x + 16$ on the accompanying set of axes. you must plot 5 points including the roots and the vertex. using the graph, determine the roots of the equation $x^2 - 10x + 16 = 0$.
click to plot points. click points to delete them.

Explanation:

Step1: Find vertex x-coordinate

For $y=ax^2+bx+c$, $x=-\frac{b}{2a}$. Here $a=1, b=-10$:
$x = -\frac{-10}{2(1)} = 5$

Step2: Find vertex y-coordinate

Substitute $x=5$ into $y=x^2-10x+16$:
$y = 5^2 -10(5)+16 = 25-50+16 = -9$
Vertex: $(5, -9)$

Step3: Find roots (y=0)

Solve $x^2-10x+16=0$. Factor:
$(x-2)(x-8)=0$
Roots: $x=2, x=8$, so points $(2,0)$ and $(8,0)$

Step4: Find 2 extra points

Choose $x=0$: $y=0-0+16=16$, point $(0,16)$
Choose $x=10$: $y=100-100+16=16$, point $(10,16)$

Step5: Identify equation roots

Roots are x-values where $y=0$

Answer:

The 5 points to plot are: $(0,16)$, $(2,0)$, $(5,-9)$, $(8,0)$, $(10,16)$
The roots of $x^2-10x+16=0$ are $x=2$ and $x=8$