Infer linear rules and connect them to intersections and models.
Free examples and worked answers. No account needed.
Practise the method.
Infer linear rules and connect them to intersections and models.
Infer linear rules and connect them to intersections and models.
Example 1
A quadratic graph has equation y=x2+bx+c. It passes through (0,33) and (1,28). A straight line passes through (0,5) and (2,15). Find both x−coordinates where the graphs meet.
Show worked answer
Answer: x=4x=7
The quadratic has c=33 and b=−6.
The line is y=5x+5.
Equating gives x2−11x+28=0
x=4 or 7.
Example 2
Machine A follows a linear rule: input 1 gives 25; input 3 gives 35. Machine B takes A's output, squares it, then subtracts 4. Find both original inputs that produce final output 896.
Show worked answer
Answer: x=2x=−10
A outputs 5x+20.
Therefore (5x+20)2=900
A's output is 30 or −30.
Solve both linear equations: x=2 or −10.
Example 3
A quadratic graph has equation y=x2+bx+c. It passes through (0,29) and (1,23). A straight line passes through (0,2) and (2,12). Find both x−coordinates where the graphs meet.
Show worked answer
Answer: x=3x=9
The quadratic has c=29 and b=−7.
The line is y=5x+2.
Equating gives x2−12x+27=0
x=3 or 9.
Put it into practice.
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