Question

Explain in your own words why a polynomial can’t be a quadratic if a= 0?

Answer 1

If
`a = 0`, then
`y = ax^2+bx+c` turns into
`y = 0x^2+bx+c`. That
`0x^2` term goes away because it turns into 0, and adding 0 onto anything does not change the expression.

So
`y = 0x^2+bx+c` turns into
`y = bx+c` which is a linear equation (b is the slope, c is the y intercept). It is no longer a quadratic as quadratic equations always graph out a curved parabola.

As an example, you could graph out
`y = 0x^2+3x+4` and note how it's the exact same as
`y = 3x+4`, both of which are straight lines through the two points (0,4) and (1,7).