Answer:
See QR code for link to Desmos
Step-by-step explanation:
The link I've provided makes graphing easy, but I'm hoping you're interested in doing this by hand. It's not that bad, and I hope you use the link to help you with what I'm about to share:
Easy point to plot: y-intercept (the y-value when x=0
h(0)=-1/5(0)^2+2(0)=0 -> (0,0) (With the link I've provided, you'll notice that the graph passes through (0,0)
Another point to plot is the vertex. Desmos shows this point to be (5,5). But without a graphing utility, there are a couple of steps you can do by hand:
- Use the axis of symmetry formula to find the x-value
- Plug in the x-value into h(x) to get the y-value.
Axis of symmetry formula:
If a quadratic is written as [tex]ax^2+bx+c[/tex], then the axis of symmetry is [tex]x=-\frac{b}{2a}[/tex].
Given that h(x)=-1/5x^2+2x, a=-1/5 and b=2. Plugging in this values into the axis of symmetry formula, we get:
[tex]x=-\frac{2}{2(-1/5)}\\=-\frac{1}{1(-1/5)}\\=5[/tex]
In desmos, type in x=5. You'll see the line cut the parabola in half. That is the axis of symmetry. The last thing to do is find the y-value. That'll give us the vertex. Plug x=5 into h(x):
h(5)=-1/5(5)^2+2(5)=-25/5+10=-5+10=5. This gives us the point (5,5).
This algorithm works with all quadratics, and I encourage you to try it out, checking your work with Desmos.
