Question

When a parabola opens upward, we call the y-value of the vertex the minimum value of the function. Why do you think we call it the minimum value?

When a parabola opens downward, we call the y-value of the vertex the maximum value of the function. Why do you think we call it the maximum value?
Pick out any quadratic equation from the lessons youÍve studied so far. Type the equation in your post and tell the vertex. Does the equation have a minimum or maximum value and what is it?

Answer 1

The vertex is the lowest point of the parabola open up, while the same point of vertex is the highest point of the parabola open downward.

The vertex as a minimum and maximum value is being point out in the attached picture.

For a quadratic equation like y = 3x^2 +12x -12 --------------- (1)

Where a = 3 and b = 12.

-b/2a gives the x-coordinate of the vertex. Hence putting values;

-12 / 2(3) = -12 / 6 = -2

Now putting x = -2 in equation (1);

y = 3(-2)^2 + 12(-2) -12

y = -24

Hence (-2,-24) is the required vertex of the parabola represented by the quadratic equation above.