Find the vertex, the y-intercept, and the x-intercepts (if any exist), and graph the function.
-The daily profit in dollars of a specialty cake shop is described by the function $\mathrm { P } ( \mathrm { x } ) = - 3 \mathrm { x } ^ { 2 } + 144 x - 1296$, where $x$ is the number of cakes prepared in one day. How many cakes are prepared per day if the company has a daily profit of zero dollars?
A) 14 cakes or 33 cakes
B) 432 cakes
C) 12 cakes or 36 cakes
D) 24 cakes

Question

Quizplus · Accepted Answer

The quadratic equation can be solved for x-intercepts (profit of zero) using the quadratic formula. Solving $-3x^2 + 144x - 1296 = 0$ gives x = 12 or x = 36.

Find the Vertex, the Y-Intercept, and the X-Intercepts (If Any P(x)=−3x2+144x−1296\mathrm { P } ( \mathrm { x } ) = - 3 \mathrm { x } ^ { 2 } + 144 x - 1296P(x)=−3x2+144x−1296

Find the Vertex, the Y-Intercept, and the X-Intercepts (If Any $\mathrm { P } ( \mathrm { x } ) = - 3 \mathrm { x } ^ { 2 } + 144 x - 1296$