Question

what is the shape of the graph of y=ax^{2} +bx+c,where a\neq 0

Answer 1

The graph of y = ax^2 + bx + c

A nonlinear function that can be written on the standard form

ax2+bx+c,wherea≠0

is called a quadratic function.

All quadratic functions has a U-shaped graph called a parabola. The parent quadratic function is

y=x2

picture51

The lowest or the highest point on a parabola is called the vertex. The vertex has the x-coordinate

x=−b2a

The y-coordinate of the vertex is the maximum or minimum value of the function.

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