Sonia graphs the equations y = –x2 + 4x and y = x – 4 to solve the equation –x2 + 4x = x – 4. her graph is shown below. what are the solutions of –x2 + 4x = x – 4? a.–5 and 0 b.–5 and –1 c.–1 and 4 d.0 and 4

Answer

C.–1 and 4

Explanation

Solving the equations  y = –x² + 4x and y = x – 4

–x² + 4x = x – 4

x² - 4x + x = 4

x² - 3x = 4

x² - 3x + (3/2)² = 4 +  (3/2)²

(x - 3/2)² = 4 +  9/4

              = 6.25

x - 3/2 = √6.25                      or  x - 3/2 = -√6.25

x = 2.5 + 1.5                                        x = -2.5 + 1.5

 = 4                                                        = -1

you have 6 cupcakes