Mathematics, 22.10.2020 14:01 michellemaricioxbyk0

Which equation is y=(x+3)^2+(x+4)^2 rewritten in vertex form?

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Answer from: makaylahamrick

y-1/2=2(x+7/2)^2

Step-by-step explanation:

Equation of the Quadratic Function

The vertex form of the quadratic function has the following equation:

y-k=a(x-h)^2

Where (h, k) is the vertex of the parabola that results when plotting the function, and a is a coefficient different from zero.

The given function is:

y=(x+3)^2+(x+4)^2

Expanding the squares:

y=x^2+6x+9+x^2+8x+16

Simplifying:

y=2x^2+14x+25

Factoring 2 from the first two terms:

y=2(x^2+7x)+25

The expression in parentheses must be completed to form the square of a binomial:

y=2(x^2+7x+49/4-49/4)+25

Isolating the square of the binomial:

y=2(x^2+7x+49/4)-49/2+25

Operating and Factoring:

y=2(x+7/2)^2+1/2

Rearranging:

$\boxed{y-1/2=2(x+7/2)^2}$

Comparing with the vertex form:

a=2, h=-7/2, k=1/2

Answer from: Quest

$y> \frac{1}{3}x$ and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be = $\frac{1-0}{3-0} = \frac{1}{3}$ .

y-intercept of dotted line is y=0 only.

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

$y> \frac{1}{3}x$ .

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

Answer from: Quest

120 seems like the most sensible answer.

step-by-step explanation:

if there is only one topping on all caramel apples and there's 120 of them. then all apples should/will be covered in sprinkles. make sense?

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