"Find b and c if the graph of..." was answered by our experts

Ean Hughes

Answered question

2022-04-12

Find b and c if the graph of the function

y = 2 x^{2} + b x + c

touches the axis Ox at the point (1;0).

zvonkurm7h

Beginner2022-04-13Added 8 answers

Step 1

y = 2 x^{2} + b x + c

passes through the point (1,0)
1)

2 + b + c = 0

Furthermore it is tangent to x-axis, so the solution x=1 must be double
Which means that the discriminant of

2 x^{2} + b x + c = 0

is zero, that is
2)

b^{2} - 8 c = 0

From (1) solve

c = - b - 2

and plug into (2)

b^{2} - 8 (- b - 2) = 0 \to {(b + 4)}^{2} = 0 \to b = - 4

and

c = 2

gsmckibbenx7ga

Beginner2022-04-14Added 17 answers

Step 1
A quadratic that touches the x axis when

x = 1

has the form

y = a {(x - 1)}^{2} = a x^{2} - 2 a x + a

Equate the coefficients to those of

2 x^{2} + b x + c

to fid b and c.

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