Answer the following for the given quadratic function. f(x)=x^2+14x+49

Question

a) what is the vertex (h,k) of f?

b) what is the axis of symmetry?

c) what are the intercepts?

Answer 1

The quadratic function f(x) = x² + 14x + 49

y = x² + 14x + 49

Compare it to parabola equation y = ax²  + bx + c

a = 1, b = 14, c = 49

Axis of symmetry is x coordinate of vertex.

• Axis of symmetry x = -b/2a

x = -14/2(1) = -7

To find y coordinate of vertex substitute x in y = x² + 14x + 49.

y = (-7)² + 14(-7) + 49

y = 49 - 98 + 49

y = 0

Vertex (h, k) = (x, y) = (-7,0)

• To find y intercept substitute x = 0 in y = x² + 14x + 49

y = (0)² + 14(0) + 49

y = 49

• To find x intercept substitute y = 0 in y = x² + 14x + 49

x² + 14x + 49 = 0

(x + 7)² = 0

x = - 7

a) Vertex (h, k) = (x, y) = (- 7, 0).

b) Axis of symmetry x = - 7.

c) x intercept is - 7 and y intercept is 49.