Question

Question 4

Consider the parabola given by the equation f(x) = -x²+2x+6
Find the following for this parabola:
A) The value of f(-1) is
B) The vertex is
C) The y-intercept is the point

Answer 1

A) f(-1) = 3

B) Vertex: (1;9)

C) y = 6

Explanation:

Given:

`f(x) = - {x}^(2) + 2x + 6`

a = -1, b = 2, c = 6

A) Replace the x with -1 in this function:

`f( - 1) = - ({ - 1})^(2) + 2 * ( - 1) + 6 = - 1 - 2 + 6 = 3`

.

B) First, let's find x vertex and then replace x with its vertex value in the given function to find y vertex:

`x(vertex) = ( - b)/(2a) = ( - 2)/(2 * ( - 1)) = ( - 2)/( - 2) = 1`

`y(vertex) = {1}^(2) + 2 * 1 + 6 = 9`

Vertex: (1;9)

.

C) The parabola will cross the y-axis when x is zero (replace x with 0 in the given function):

`- {0}^(2) + 2 * 0 + 6 = 0 + 0 + 6 = 6`

y = 6