Question

Which equation has this graph?
y = x2 - 6x + 5
y = -x2 - 6x + 5
y = -x2 - 6x - 5
y = x2 + 6x - 5

Answer 1

which equation has a minimum point at (3,-4) ?
You can exclude B and C, because those open down, and have no minimum point.

So either A or D.

For A,
\(\large\color{black}{ y = x^2 - 6x + 5 }\)
\(\large\color{black}{ y =(x^2 - 6x)+ 5 }\)
\(\large\color{black}{ y =(x^2 - 6x+9-9)+ 5 }\)
\(\large\color{black}{ y =(x^2 - 6x+9)+ 5-9 }\)
\(\large\color{black}{ y =(x-3)^2-4 }\)

For D
\(\large\color{black}{ y = x^2 - 6x - 5 }\)
\(\large\color{black}{ y =(x^2 - 6x)- 5 }\)
\(\large\color{black}{ y =(x^2 - 6x+9-9)- 5 }\)
\(\large\color{black}{ y =(x^2 - 6x+9)- 5-9 }\)
\(\large\color{black}{ y =(x-3)^2-14 }\)

Answer 2

So which one do you think has the minimum point at (3,-4) and therefore, which one is the equation of the blue graph ?