Question

A graph has the equation y=x²+px+r where p and r are constants. The graph passes through the points (0,4), (1,3) and (8,w) Work out the value of w.

Answer 1

By substituting the given points into the equation y=x²+px+r, we solve for constants p and r, and then determine the value of w, which is 60 when x=8.

Step-by-step explanation:

The student's question relates to finding the value of 'w' for a quadratic function that passes through the points (0,4), (1,3), and (8,w). The given equation for the graph is y=x²+px+r where p and r are constants. By substituting the known points into the equation, we can determine the values of p and r and then use them to find the value of 'w' when x=8.

Step-by-Step Solution:

1. Substitute (0,4) into the equation: 4=0²+p(0)+r which simplifies to r=4.
2. Substitute (1,3) into the equation: 3=1²+p(1)+4 which simplifies to p=-1.
3. The quadratic equation becomes y=x²-x+4.
4. Finally, substitute x=8 to find the value of 'w': w=8²-8+4 which gives w=64-8+4 leading to w=60.