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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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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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Solve the simultaneous equations 3x + 2y = 12 and 10y = 7x + 16

First we need to rearrange both equations into the form ax + by = c (where a, b and c are the integers). We can label these 1. and 2.We then have:3x + 2y = 12 1.7x -10y = -16 2.In order to find the x valu...

Answered by Anjali A. • Maths tutor

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The width of a rectangle is X cm.  The length is 1·5 cm more than the width.  The perimeter of the rectangle is 17 cm. Write down an equation satisfied by X  and solve it to find X.

Let's call the length 'L', and the width 'X'. Since the length is 1.5cm more than width, we can form the equation: L = X + 1.5 (Equation 1)Let's call the perimeter 'P'....

Answered by Oliver D. • Maths tutor

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