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The point (-3, -4) is the turning point of the graph of y = x^2 + ax + b, where a and b are integers. Find the values of a and b.

The function y = x² + ax + b is a quadratic polynomial and therefore has one turning point. The turning point of a quadratic graph is either the maximum or minimum point. The coefficient of x

Answered by Oliver L. • Maths tutor

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Integrate sin^2(x)

sin^2(x) is not one of the functions whose antiderivative is commonly known to us. When we see trigonometric functions our best bet is usually to think of some trigonometric identity we know. In this case...

Answered by John P. • Maths tutor

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A circle with center C has equation x^2 + y^2 + 8x - 12y = 12

Circle equation = (x - a)²+ (y - b)² = r²Where Centre coordinates (a, b) and radius 'r'Therefore x² + y² + 8x - 12y = 12 is to be rewritten in this ...

Answered by Henry K. • Maths tutor

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Expand and simplify (x − 4)(2x + 3y)^2

Rewrite (x − 4)(2x + 3y)² as (x - 4)(2x + 3y)(2x + 3y)
Multiply out the first two brackets to give -(2x²+ 3xy - 8x² - 12y)(2x + 3y)
Multiply o...

Answered by Henry K. • Maths tutor

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Find the values of x and y when 3x+4y=18 and 4x+2y=14

Label equations: (a) 3x+4y=18(b) 4x+2y=14We need to be able to cancel out either the x's or the y's. The simplest choice is to double (b) so that we can cancel out the y's.2 x (b) : 8x+4y=28 (Give this a ...

Answered by Rosie E. • Maths tutor

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