Maths homework help with parabolas

The equation of a parabola is y=ax2+bx+c
A parabola crosses the y-axis at (0,7) and passes through (2,5) and (5,42).
Find the values of a, b and c.

I mainly need to know how to know how to work it out, but the answer is always nice. Thanks!

Substitute the values we know into the equation and the first result is clear and obvious.

For (0,7), we get 7 = 0² + 0 + c

So c = 7

For (2, 5), we get 5 = 4a +2b + 7........(i)

For (5, 42), we get 42 = 25a + 5b + 7 .......(ii)

Solve (i) and (ii) as simultaneous equations, to find and a and b

This gives a = 2.66rec and b = 6.33rec using decimals

Therefore the equation is y=2.67x² + 6.33x + 7

or y=8x²/3 + 19x/3 + 7 using vulgar fractions

or y = (8x² + 19x + 21)/3 using the common factor.

OK?