Question

Here is a sketch of y=x^2+bx+c The curve intersects

Answer 1

Answer:

y = 18  and  x = -2

Step-by-step explanation:

y = x^2+bx+c   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     Plugging in  (2,0) :

y=x2+bx+c  

0=(2)^2+b(2)+c  

y=4+2b+c  

-2b=4+c  

b=-2+2c  

Plugging in  (0,−14) :

y=x2+bx+c  

−14=(0)2+b(0)+c  

−16=0+b+c  

b=16−c  

Now that we have two equations isolated for  b , we can simply use substitution and solve for  c .   y=x2+bx+c  16 + 2 = y   y = 18  and  x = -2