Determine the vertex of the following quadratic functions Ex

Determine the vertex of the following quadratic functions. Express your answer as an ordered pair in the form (x,y) (x,y) . a.g(x)=(8x+3)(4x10) b.j(x)=x^210^2 c.p(x)=x^2+5x5

Solution

a . g(x) = (-8x+3)(4x-10) = -32x^2+92x-30

Vertex x = -b/2a = -92/(2*-32) = 92/64 = x = 23/16

replace x = 23/16 into g(x), this gives y = 289/8

so (23/16,289/8)

b) j(x) = x^2-10^2

here since b = 0

x = = 0 so y = j(0) = -100

(0,-100)

c) -x^2+5-5

x = -b/2a = -5/2(-1) = 5/2

y = p(5/2) = 5/4

vertex is at (5/2,5/4)