Question

Lindsay is creating a bridge out of dried pasta and glue. In her plans, she sketches the graph to determine the lengths of the noodles, in centimeters, needed for the arch to increase the length of the bridge in 1 centimeter increments. Which function did Lindsay use to create her design? f(x) = (x – 5)2 + 8 f(x) = –(x + 5)2 + 8 f(x) = 0.5(x + 5)2 + 8 f(x) = –0.5(x – 5)2 + 8

Answer 1

From the graph shown it can be seen that the bridge is represented by a parabola with vertex of (5, 8) and roots of 1 and 9.

Recall that the vertex form of the equation of a parabola with vertex (h, k) is given by
$y=a(x-h)^2+k$

Thus, the equation of the given graph in vertex form is given by
$y=a(x-5)^2+8$

Also, recall that the equation of a parabola with roots, p and q, is given by
$y=a(x-p)(x-q)$

Thus the equation of the given graph can be given by
$y=a(x-1)(x-9)$

To get the value of a, we equate both equations and solve as follows:
$a(x-5)^2+8=a(x-1)(x-9) \\ \\ a(x^2-10x+25)+8=a(x^2-10x+9) \\ \\ ax^2-10ax+25a+8=ax^2-10ax+9a \\ \\ 25a-9a=-8 \\ \\ 16a=-8 \\ \\ a=- \frac{8}{16} =- \frac{1}{2}$

Therefore, the function that Lindsay used to create her design is
$f(x)=-0.5(x-5)^2+8$

Answer 2

Answer:

f(x)= -0.5(x-5)^2+8