Consider the function f(x) = 2x² + 6x - 8

Part A.What is the vertex form of f(x)? A.) f(x) = 2(x - 3)² - 4 B.) f(x) = 2(x + 3)² + 4 C.) f(x) = 2(x - 1.5)² - 12.5 D.) f(x) = 2(x + 1.5)² - 12.5 |
Part B.What is the factored form of f(x)? A.) f(x) = (2x + 1)(x - 8) B.) f(x) = (2x - 1)(x + 8) C.) f(x) = 2(x + 4)(x - 1) D.) f(x) = 2(x - 4)(x + 1) |

Part A.Vertex form is f(x) = a(x - h)² + k(h,k) are the (x,y) coordinates of the vertex To find the x-coordinate of the vertex, find -b/2aIn f(x) = 2x² + 6x - 8, a = 2, b = 6, and c = -8 -b ---- 2a = -6 ---- 2(2) = -6/4 x = -1.5 To find the y-coordinate of the vertex,substitute -1.5 back in for x. y = 2(-1.5)² + 6(-1.5) - 8 = 2(2.25) - 9 - 8 = 5.5 - 9 - 8 = -12.5 The vertex is (-1.5, -12.5). Therefore, vertex form is D.) f(x) = -2(x + 1.5)² - 12.5Ask Algebra House |
Part B.Factor f(x) = 2x² + 6x - 8 = 2(x² + 3x - 4) {factored 2 out} = 2(x + 4)(x - 1) {factored into two binomials} C.) f(x) = 2(x + 4)(x - 1) |