Question

Given a quadratic function, f(x) = ax 2 + bx + c has a positive leading coefficient and the vertex that has a y-coordinate of zero. Determine the number of real zeros of the function.

Answer 1

the graph will open upwards because of the positive leading coefficient.

The graph will just touch the x axis once because of the y coordinate of the zero.

There will be one value of the zero duplicity 2.

2 real zeroes

Answer 2

Explanation:

Given a quadratic function,
`f(x) = ax^2 + bx + c`

The leading term a>0 and also vertex has y coordinate 0

Since y coordinate is 0, vertex lies on x axis.

Since leading coefficient is positive, the parabola is open upward touching the x axis.

Since the parabola touches the x axis, we find that there are two equal roots for this equation.

i.e. there is one real zero with multiplicity 2.