Consider the parabola given by the equation: f(x) = 4x² - 6x - 8 find the following for this parabola: a) the vertex: preview b) the vertical intercept is the point preview c) find the coordinates of the two a intercepts of the parabola and write them as a list, separated by commas: preview it is ok to round your value(s) to to two decimal places. get : video video

The vertex:

The vertical intercept is:

The coordinates of the two intercepts of the parabola are and

Step-by-step explanation:

To find the vertex of the parabola you need to:

1. Find the coefficients a, b, and c of the parabola equation

2. You can apply this formula to find x-coordinate of the vertex

, so

3. To find the y-coordinate of the vertex you use the parabola equation and x-coordinate of the vertex ()

To find the vertical intercept you need to evaluate x = 0 into the parabola equation

To find the coordinates of the two intercepts of the parabola you need to solve the parabola by completing the square

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1