Can I get some help please? Thanks!

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2 Answers
Sep 10, 2017

(D)"

Explanation:

"the equation of a parabola in "color(blue)"vertex form" is.

color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))
where (h , k ) are the coordinates of the vertex and a is a multiplier.

• " if "a>0" then minimum turning point " uuu

• " if "a<0" then maximum turning point " nnn

"here "a=2>0rArr" minimum turning point"

y=2(x+2)^2-3" is in vertex form"

rArrcolor(magenta)"vertex "=(-2,-3)

2(x+2)^2>=0" for all real x"

rArr"minimum value "=-3

y" is defined for all real values of x"

rArr" domain is " x inRR

"range is "y inRR,y>=-3
graph{2(x+2)^2-3 [-10, 10, -5, 5]}

Sep 10, 2017

Graph of shape uu

"Minimum "->"Vertex"->(x,y)=(-2,-3)
Thus y_("minimum")=-3

Input color(white)(.)->" Domain "->x->(-oo,+oo) in RR
Output->" Range "color(white)("d")->y->[-3,+oo) in RR-> RR>=-3

THUS D

Explanation:

Given: y=2(x+2)^2-3

This is the vertex form of a quadratic (completing the square).

If you were to expand the bracket your first term would be +2x^2

As this is positive the graph is of form uu thus the vertex is a minimum.

Consider the standardised form of y=a(x+color(red)(b/(2a)))^2+color(green)(k)

Then color(white)(..)x_("vertex")= (-1)xxcolor(red)(b/(2a))color(white)(..) and color(white)(..) y_("vertex")=color(green)(k)

So we have "Minimum "->"Vertex"->(x,y)=(-2,-3)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
This is one way to remember the relationship

Input color(white)(..)comes before Output
D color(white)("dddd.")comes before color(white)(.) R
Domain comes before Range

Input color(white)(.)->" Domain "->x->(-oo,+oo) in RR
Output->" Range "color(white)("d")->y->[-3,+oo) in RR -> -3<=y

Tony BTony B