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the graph of the parabola x=2y^2-6y+3 has an x-intercept (a,0) and two y-integers (0,b) and (0,c). Find a+b+c​

User Trees
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1 Answer

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9514 1404 393

Answer:

6

Explanation:

The sum of the roots (y-intercepts) of the polynomial is the opposite of the ratio of the linear term coefficient and the leading coefficient.

b + c = -(-6/2) = 3

The x-intercept is the constant: a = 3

Then the sum a+b+c is ...

a + (b +c) = 3 + 3 = 6

_____

Additional comment

The factored form of the polynomial for the given intercepts will be ...

x = 2(y -b)(y -c)

and the expanded form of that is ...

x = 2y^2 -2(b+c)y +2bc

The y-coefficient is ...

-2(b+c) = -6

b +c = 3 . . . . . . . divide by -2. This is the result used above.

We show the graph so you can add up the values of the intercepts to see that the sum is 6.

the graph of the parabola x=2y^2-6y+3 has an x-intercept (a,0) and two y-integers-example-1
User Joe G Joseph
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