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A parabola is (mathematically speaking) a quadratic function, which looks like this y = ax2 + bx + c where a, b and c are constants. (If three points on the curve are known, then a, b and c can be found.) The gradient, then, can be found by differentiation: dy/dx = 2ax + b A parabola has one maximal or minimal point, where the gradient is zero. 2ax + b = 0 x = -b/2a Use the original function to find the corresponding value of y: y = a(-b/2a)2 + b(-b/2a) + c = b2/4a - b2/2a + c = c - b2/4a So the coordinates of your turning point are ( -b/2a , c - b2/4a ) This result can also be derived by completing the square.

Q: Can you predict the maximum or minimum point on a parabola?

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When you look at the parabola if it opens downwards then the parabola has a maximum value (because it is the highest point on the graph) if it opens upward then the parabola has a minimum value (because it's the lowest possible point on the graph)

Apex.

the vertex, or very bottom point.I can also be called the maximum or minimum.

The maximum point.

You set the derivative equal to zero and solve the equation. For example y = x^2 + 5x +7 is the equation of a parabola. dy/dx = 2x +5. Setting 2x +5 = 0 then x = -5/2. When x = -5/2 y = 3/4. This is the minimum. We know it's a minimum and not a maximum because when x is large y is large.

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The vertex, or maximum, or minimum.

The point on the parabola where the maximum area occurs is at the vertex of the parabola. This is because the vertex represents the maximum or minimum point of a parabolic function.

When you look at the parabola if it opens downwards then the parabola has a maximum value (because it is the highest point on the graph) if it opens upward then the parabola has a minimum value (because it's the lowest possible point on the graph)

Apex.

There's the vertex (turning point), axis of symmetry, the roots, the maximum or minimum, and of course the parabola which is the curve.

the vertex, or very bottom point.I can also be called the maximum or minimum.

It is either a maximum or minimum value depending on its downwards shape or its upwards shape

if it opens up then the point is called the minimum if it opens down its called the maximum

If you mean a parabola with a maximum point then it will look like an umbrella.

The maximum point.

maximum point :)

maximum point :)