Quadratic Function (1 Viewer)

[letsdie45]

Hi can someone help me out with this question.

Find a, b and c if the graph of the quadratic function f(x) = ax^2+bx+c passes through O (0,0), A (4,0) and B (5,5). Then check by substitution whether the point D(-2,10) lies on the curve.

Thanks.

 

[Timothy.Siu]

Hi can someone help me out with this question.

Find a, b and c if the graph of the quadratic function f(x) = ax^2+bx+c passes through O (0,0), A (4,0) and B (5,5). Then check by substitution whether the point D(-2,10) lies on the curve.

Thanks.

u sub in those points to get simultaneous equations,
immediately u know c=0 from the first point, then u get 2 equations,
16a+4b=0 and 25a+5b=5
then solve them, a=1 b=-4
f(x)=x^2-4x
then test the point, and from what i got, it doesn't lie on the curve, not sure if i did it right then.

 

[Makro]

don't have that much time to work it out. Sub in all those points until you find a value for a pronumeral rather than equation. You then sub that value back into the 2 other equations you've found. Then you'd be left with 2 equations. Solve them simulateneously to find a and then b.

Not sure about the check by subbing part..

 

[3.14159potato26]

Find a, b and c if the graph of the quadratic function f(x) = ax^2+bx+c passes through O (0,0), A (4,0) and B (5,5). Then check by substitution whether the point D(-2,10) lies on the curve.

A different method that doesn't involve simultaneous equations is by observing that the value of the x-intercepts are already given, i.e. roots are x = 0,4. Therefore,
Sum of roots = 0 + 4 = 4
Product of roots = 0 * 4 = 0.
By definition, f(x) = x^2 - (Sum of roots)x + (Product of roots)
f(x) = x^2 - 4x.
By testing the x-values, all the points ( even (5,5) ) lie on it, therefore f(x) = x^2 - 4x is the correct answer.

 

[letsdie45]

ok thank you people!