Question

The value of a in y=ax2+bx+c and the vertex of the parabola are given. How many x-intercepts does the parabola have? Explain how you arrived at this number.a= -3; vertex at (2,4)The parabola has x-intercept(s), because the parabola opensand the vertex isthe x-axis.

Answer 1

Given: The value of a in y=ax2+bx+c and the vertex of the parabola are given.

a= -3; vertex at (2,4)

Required: How many x-intercepts does the parabola have? Explain how you arrived at this number.

Step-by-step explanation:

Parabola is of form

`(x-h)^2=4a(y-k)`

And a here is negative.

So definitely it is a downward parabola.

The vertex is (2,4), it lies in 1st quadrant, so it is above x-axis.

Since parabola is going downward, it will cut x- axis at two points. (By putting y = 0 we get quadratic in x. So two solutions are there.)

Hence there are 2 intercepts.

Final Answer: Parabola opens downwards, vertex is above x-axis and there are 2 x-intercepts.