Graph quadratic functions in standard form

Question

Consider the quadratic function below and (a) find the vertex : (b ) find the axis of symmetry : (c) determine whether there is a maximum or a minimum value and find that value : and (d) graph the function .

f(x) =x^2-16x+55

A) the vertex occurs at___

B) Find an equation for the axis of symmetry

Answer 1

Vertex at x = 16 / 2

Answer 2

x^2 -16x +55

take the derivative, set it =0

solve for x to get the x coordinate of the vertex

2x-16=0

2x =16

x= 8

8^2 -16(8) -55= -64-55= -119

vertex is (8, -119)

axis of symmetry is x=8

the graph is an upward opening parabola with minimum point = vertex (8,-119)

y intercept is the constant term = 55

x intercepts are found using the quadratic formula = 16/2+ or - (1/2)sqr(16^2 -4(55))

= 8 + or - 18 = -10 or 26 = the two points (-10, 0) and (26,0)

that gives 4 points to connect with a smooth parabolic curve

there's also a 5th point symmetric about x=8. Since (0,55) is on the parabola, also (16,55) is on the parabola