how does one work out the maximum point by completing the square
thnks reply quickly plz
osmosis786
For the quadratic equation: $\displaystyle ax^2+bx+c = 0$
Divide through by a: $\displaystyle x^2+\frac{b}{a}x + \frac{c}{a} = 0$
Take c/a from both sides: $\displaystyle x^2+\frac{b}{a}x = -\frac{c}{a}$
Then make it into the form (ax+b)^2 and add b^2 to both sides: $\displaystyle (x+\frac{b}{2a})^2 = \frac{b^2}{4a^2} -\frac{c}{a} = \frac{b^2-4ac}{4a^2}$
Can you go from there?
how do i find the maximum point of this equation using completing the square
7x + 15 − 2x^2
can u please help as i know how to do minimum points but not maximum points thanks you
???? I thought the method in finding the minimum point or the maximum point of a quadratic is the same -- you put the equation into the form $\displaystyle y = a(x - h)^2 + k$ by completing the square. It's just that when the leading coefficient is positive the vertex is the minimum point, and when the leading coefficient is negative the vertex is the maximum point.
$\displaystyle y = 7x + 15 - 2x^2$
$\displaystyle y = -2x^2 + 7x + 15$
$\displaystyle y = -2\left(x^2 - \frac{7}{2}x\right) + 15$
Now complete the square. When you can get the quadratic into the form
$\displaystyle y = a(x - h)^2 + k$, the vertex is (h, k).
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