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true or false1. For any quadratic function with real coefficients, = ^2 + + , the x-coordinate of the vertex may be readily calculated by the formula -b/(2a)

User Maharshi
by
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1 Answer

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Given quadratic equation is


y=ax^2+bx+c

The graph of a quadratic function is a parabola with vertex at (h,K).

The general equation of the parabola is


y=m\cdot(x-h)^2+k

write the given equation in the form


y=m(x-h)^2+k
\begin{gathered} y=ax^2+bx+c \\ y=a(x^2+(b)/(a)x)+c \\ y=a(x^2+2(x)((b)/(2a))+((b)/(2a))^2)+c-a\cdot((b)/(2a))^2 \\ y=a\cdot(x+(b)/(2a))^2+c-a\cdot((b)/(2a))^2 \\ y=a\cdot(x-(-(b)/(2a)))^2+c-(b^2)/(2a) \end{gathered}

So, the x- coordinate of the vertex is


x=-(b)/(2a)

So, it is true.

User Shir
by
6.3k points
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