Question

The graph of y = x² is the solid black graph below. Which

function represents the dotted graph?
A.y=(x+5)*2+2
B.y=(x+5)*2-2
C.y=(x-5)*2-2
D.y=(x-5)*2+2

Answer 1

y=(x+5) ^2+2 The correct answer is option A. You can check your answer by graphing the functions using a parabola calculator like desmos graphing calculator
To actually solve it

The general form of a quadratic function is:
y=a(x−h)2+k

Where (h,k) is the vertex of the parabola, and a determines the width and direction of the parabola. If a>0, the parabola opens upward, and if a<0, the parabola opens downward1.
To find the equation of the dotted graph, we need to compare it with the solid black graph, which has the equation y=x^2

. We can see that the dotted graph has the same shape and direction as the solid graph, so the value of a is the same, which is a=1 We can also see that the dotted graph has shifted left by 5 units and up by 2 units, compared to the solid graph. This means that the vertex of the dotted graph is at (−5,2) so h=−5 and k=2. Therefore, the equation of the dotted graph is:
Y=(x-(-5))^2+2
Y=(x+5)^2+2