Question

For a parabola with a minimum point at (3,-1), determine the equation for the function's axis of symmetry

Answer 1

x = 3

Explanation:

Since the parabola has a minimum turning point then it is a vertically opening parabola with a vertical line of symmetry.

The line of symmetry passes through the turning point and has equation

x = c

where c is the value of the x- coordinate of the minimum point, that is

Equation of symmetry is x = 3

Answer 2

x=3

(Do not write a character less than what I have written; 3 is not the answer but x=3 is the answer.)

Explanation:

Parabolas have a axis of symmetry; this is the line they are symmetrical about.

The line of symmetry will always go through the vertex.

Since your question says it is a function the line will be vertical and will be of the form x=a number.

The number is determine by the x-coordinate of the vertex.

I know the vertex of your problem is (3,-1) because it says that is the minimum point of the graph. The vertex of a parabola will always be it's maximum (this parabola is open down) or minimum (this parabola is open up).

So the axis of symmetry is just:

x=3.

You must actually write x=3.

3 is not the answer.

x=3 is the answer.

Little note down here:

(If it had said the parabola wasn't a function, the axis of symmetry would have been horizontal and therefore of the form y=a number where the number was the y-coordinate of the vertex.)