Graph the parabola.
Y = 4x^2 + 7

In Picture Below:

Step-by-step explanation:

To graph:

1. find the y intercept of the equation (y=4x^2+7, let x =0, y=4*0 +7 which equals y=7)

2. find the x intercepts (if there are any); y=4x^2+7, let y =0, 0=4x^2+7, 4x^2=-7, therefore no x intercepts (you cannot root a negative)

3. find vertex using -b/2a formula, a=4 b=0 c=7, therefore x =0, sub that into y=4x^2+7, y=7, therefore vertex is (0,7)

4. graph all this information

step-by-step explanation:

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.