Here is a sketch of y=x^2 + bx + c. the curve intersects the x-axis at (2,0) and point p. the y-axis at (0,14) work out the x-coordinate of the turning point of the graph

To find the turning point, or vertex, of this parabola, we need to work out the values of the coefficients b and c.

We are given two different solutions of the equation.

First, (2, 0). 


Second, (0, 14).


So we have a value (14) for c. We can substitute that into our first equation to find b.



We can now plug in our values for b and c into the equation to get its standard form.



To find the vertex, we can convert this equation to vertex form  by completing the square.









Thus, the vertex is (4.5, –6.25).

We can confirm the solution graphically (see attachment).