What is the standard form of the equation y = 1/2 (x - 4)^2 + 6 a) y= 1/2 x^2 − 8x + 22 b) y= 1/2 x^2 − 4x + 22 c) y= 1/2 x^2 − 4x + 14 d) y= 1/2 x^2 − 8x + 14 which equation represents the quadratic parent function shifted to the left two units? a) y=(x−2)^2 b) y=(x+2)^2 c) y=x^2 − 2 d) y=x^2 + 2 find the equation, in vertex form, for a parabola with a vertex of (2,-5) that goes through the point (3,4). y=.36(x+2)^2−5 y=2(x−2)^2−5 y=.75(x−2)^2−5 y=9(x−2)^2−5

1) The standard form for any equation is

with this said we have to get the equation that they gave us into this form so we have

this means that the order of operations we have to follow is PEMDAS to get it to the standard form
Parentheses
Exponent
Multiplication
Division
Addition
Subtraction

or option C in this case.

2) The quadratic parent function is

in general if you want to move the parent function to move to the left r units you will have

so in this case you will have

3)

The equation to find the vertex is

since the paranola has vertex (2,-5) we have

to solve for a, we plug the values (3,4) into the equation and have the following


once we have the value for a, we plus it into the previous equation to get the equation of a parabola with the desired vertex and that passes through the desired point so