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

4 0

2 years ago

Directed line segment AB has endpoints A(2,3) and B(8,15). Point P has coordinated P(6,11). What ratio does P partition AB into?

Vladimir79 [104]

Refer to the graph shown below. It confirms that points A, B and P are
collinear.

Calculate the length of AP (as a).
a = √[(6 - 2)² + (11 - 3)²]
= 8.9443

Calculate the length of BP (as b).
b = √[(8 - 6)² + (15 - 11)²]
= 4.4721

Calculate ratio a/b.
a/b = 8.9443/4.4721 = 2
Therefore P partitions AB in a 2:1 ratio so that AP = 2*BP.

Answer: 2:1 ratio.

7 0

2 years ago

Why do we need to know about unit rates

allochka39001 [22]

Answer:

because they allow us to make direct comparisons

Step-by-step explanation:

8 0

2 years ago

What is the coefficient in the expression 10x + 8 I need help

koban [17]

Answer:

Step-by-step explanation:

A coefficient is a multiplicative factor. Whatever is in front of the variable is a coefficient

5 0

3 years ago