HELP ASAP 25 POINTS

g(x) = x² + 4x + 5

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

Here (h, k ) = (- 2, 1 ), thus

y = a(x + 2)² + 1

To find a substitute (0, 5) ← y- intercept into the equation

5 = a (0 + 2)² + 1 ( subtract 1 from both sides )

4 = 4a ( divide both sides by 4 )

a = 1

g(x) = (x + 2)² + 1 ← in vertex form

Expand parenthesis and simplify

g(x) = x² + 4x + 4 + 1, then

g(x) = x² + 4x + 5 ← in standard form

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

step-by-step explanation:

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