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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.
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How do you know if a parabola has a minimum or maximum value?
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)
What is another name for the maximum or minimum point of a quadratic graph?
Apex.
What is The turning point of a parabola?
the vertex, or very bottom point.I can also be called the maximum or minimum.
If the parabola opens downward the vertex is called the?
The maximum point.
How do you find the maximum or minimum point of a parabola?
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.
