Question

Consider the parabola given by the equation: f(x) = 2x2 + 14.0 – 4

Find the following for this parabola:
A) The vertex:
B) The vertical intercept is the point
C) Find the coordinates of the two z intercepts of the parabola and write them as a list, separated by
commas:
It is OK to round your value(s) to to two decimal places.

Answer 1

Explanation:

f(x) = 2x² + 14x - 4

= 2(x² + 7x) - 4

= 2(x² +7x + 3.5²) - 2(3.5²) - 4

= 2(x+3.5)² - 28.5

vertex (3.5, -28.5) = (7/2, -57/2)

The vertical intercept is the y-intercept, i.e., f(0) = -4.

The x-intercepts are the values of x for which y=0.

2x² + 14x - 4 = 0

x = [-14±√(14²-4(2)(-4))]/[2(2)] = [-7±√57]/2 ≅ -7.27, 0.27