graph the function $f(x) = x^2 - 10x + 15$.\nplot the vertex. then plot another point on the parabola. if…

graph the function $f(x) = x^2 - 10x + 15$.\nplot the vertex. then plot another point on the parabola. if you make a mistake, you can erase your parabola by selecting the second point and placing it on top of the first.

graph the function $f(x) = x^2 - 10x + 15$.\nplot the vertex. then plot another point on the parabola. if you make a mistake, you can erase your parabola by selecting the second point and placing it on top of the first.

Answer

Explanation:

Step1: Find vertex x-coordinate

For quadratic $ax^2+bx+c$, $x=-\frac{b}{2a}$ $a=1, b=-10$, so $x=-\frac{-10}{2(1)}=5$

Step2: Find vertex y-coordinate

Substitute $x=5$ into $f(x)$ $f(5)=(5)^2 -10(5)+15=25-50+15=-10$

Step3: Find a second point

Choose $x=0$, substitute into $f(x)$ $f(0)=(0)^2 -10(0)+15=15$

Step4: Find symmetric point (optional)

Symmetric to $(0,15)$ over $x=5$ is $(10,15)$ $f(10)=(10)^2 -10(10)+15=100-100+15=15$

Answer:

  1. Vertex point: $(5, -10)$
  2. Additional point: $(0, 15)$ (or $(10, 15)$) Plot these points and draw a parabola opening upwards through them.