****40 points and the brainliest. HELP QUICK ******A company plans to sell bicycle helmets for $26 each. The company's business manager estimates that the cost, y, of making x helmets is a quadratic function with a y-intercept of 8,400 and a vertex of (500, 15900)x= number of helmetsy = amount in dollarsWhich system models this situation?a) y = 26x and y = 8,400(x-500)2+15,900b) y = 26x and y = -0.030(x-500)2+15,900c) y = x/26 and y = -0.030(x-500)2+15,900d) y = x/26 and y =8,400(x-500)2+15,900
Accepted Solution
A:
Given from the question Vertex (h,k) = (500, 15900) One of the points on the graph (x,y) = (0,8400)
FIRST PART: Find the quadratic function We can find the quadratic function by this formula y = a (x - h)² + k
Input the numbers to the formula, to find the value of a y = a (x - h)² + k 8400 = a(0 - 500)² + 15900 8400 = a (500)² + 15900 8400 = 250000a + 15900 -250000a = 15900 - 8400 -250000a = 7500 a = 7500/-250000 a = 0.03
Submit a to the formula y = a (x - h)² + k y = 0.03 (x - 500)² + 15900 (This is the quadratic function)
SECOND PART: Find the linear function the total cost = cost each helmet × the number of helmet y = 26x