Quadratic - Extreme Values

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Minimum and maximum values of $$ax^{2}+bx+c=0$$ :

  • If a > 0: minimum value = $$\frac{4ac - b^2}{4a}$$ and occurs at x = $$\frac{-b}{2a}$$

  • If a < 0: maximum value = $$\frac{4ac - b^2}{4a}$$ and occurs at x = $$\frac{-b}{2a}$$

Question 1

A quadratic equation f(x) reaches its minimum when x= -1 and equals 1. If f(0) equals 4, what is f(8)?

Question 2

If 'a' and 'b' are the roots of the equation $$x^{2} - (t-3)x - t - 2 =0$$. What is the minimum value of $$a^{2} + b^{2}$$?

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Quadratic - Extreme Values

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