Need help. I could not paste the graph for this problem but there is a hint and equation. Please help !!!?

Question

Look at the graph above and comment on the sign of D or the discriminant. Form the quadratic equation based on the information provided and find its solution.

The equation is

y = ax^2 + bx + c

One approach: Put each (x, y) pair that you have in to get three equations. Then solve them to find a, b, and c.

A different approach: If (s,0) and (t,0) are where the parabola crosses the x-axis, then the equation is y = a(x - s)(x - t)
To find a, put that vertex you are given in to find the equation.

Answer 1

If a parabola intersects the x-axis in two places, the discriminant is positive. If it's tangent (intersects at the vertex) the discriminant is zero. If it doesn't intersect the x-axis, the discriminant is negative.

For the rest of it, were you given some specific points on the parabola?

Answer 2

If the graph does not cross the x-axis, then D is negative. Ifthgraph just touches (is tangent to) the x-axis, then D = 0. If the graph crosses the x-axis twice the D is positive.

If you are given the two points where the graph crosses the x-axis then the equation is y= (x-s)(x-t). There is no a in the equation

If the equation is ax^2+bx+c then D = b^2 -4ac.
The axis of symmetry is x = -b/2a. The vertex lies on the axis of symmetry. If a is negative, the parabola will have a max value at the vertex and be shaped like ann upside down U.
If a is positive , then the parabola will have a minimum value at the vertex and be shaped like a U.