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# find b and c

find b and c so that y= 10x2+bx+c has vertex (5,-4)

### 3 Answers by Expert Tutors

4.9 4.9 (216 lesson ratings) (216)
1

Line of symmetry is where the vertex lies.

X = -b/2a = -b/20

In this case x = 5 since the vertex has coordinates (5, -4)

5 = -b/20

-b = 100

b = -100

To find c we input b and the coordinates of the vertex in the original equation.

-4 = 10(5)^2 - 100(5) + c

-4 = 250 - 500 + c

-4 = -250 + c

c = 246

Thank you Muhammad.  I learned something.
Scott S. | No stress math tutorNo stress math tutor
5.0 5.0 (304 lesson ratings) (304)
0
Standard form of parabola is y = ax2 + bx + c
Vertex form of parabola is y = a(x-h)2 + k where (h,k) is the vertex.

a is the same in each equation, which is given as 10, and if we also plug in the vertex given we get (in vertex form)

y = 10(x-(5))2 + (-4)

Now we just need to rewrite this in standard form to find b and c.

First, foil the (x-5)2

10(x-5)(x-5) - 4

10(x- 5x - 5x + 25) - 4

10(x2 - 10x + 25) - 4

Distribute the 10

10x2 - 100x + 250 - 4

Finally,
10x2 - 100x + 246 shows b=-100 and c=246
Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
0

The formula to use is:

Y = a ( X - b/ 2a )2  -  ( b-4ac ) / 4a2

Y = 10( X - 5 ) 2  - 4

Y =10[ ( X - 10X + 25 ) - 4 ]

Y = 10 X2 - 100X + 250 -40

Y = 10 X -100X + 210

another method:

-b / 2a = 5          -b/20 = 5        b = -100

b- 4ac = 4         [ (-100) - 4 (10)(c) ] / 4 (10) 2 = 4

10000 - 40c / 4 ( 100) =4

10000 -40c = 1600
8400 = 40 c

C = 210

ax2 + bx+c 10X2 -100X + 210-

any quadratic in the form of aX2 + bX + c can be written equivalently as
a[( X - b/ 2a)2 - (b-4ac)/4a2