Question 1163445
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Let x be the numbet of years since 1980 and y be the life expectancy for a person born between ( 1980 + x ) and ( 1980 + x + 5 ). Find the quadratic equation whose graph passess through the points  {{{cross("( 0, 78,2)")}}} (0,78.2), ( 5, 79) and ( 10, 79.2 )<br>
The general quadratic function is<br>
{{{y = ax^2+bx+c}}}<br>
Use the three given data points in that equation to form three equations in the coefficients a, b, and c.<br>
{{{a(0^2)+b(0)+c = 78.2}}}
(1) {{{c = 78.2}}}<br>
{{{a(5^2)+b(5)+c = 79}}}
(2) {{{25a+5b+c = 79}}}<br>
{{{a(10^2)+b(10)+c = 79.2}}}
(3) {{{100a+10b+c = 79.2}}}<br>
Substitute (1) into (2) and (3) to get two equations in a and b.<br>
(4) {{{25a+5b = 0.8}}}
(5) {{{100a+10b = 1}}}<br>
Subtract (4) from (5).<br>
{6) {{{75a+5b = 0.2}}}<br>
Subtract (4) from (6).<br>
{{{50a = -0.6}}}<br>
(7) {{{a = -0.012 = -3/250}}}<br>
Substitute in (4) to find b.<br>
{{{25(-3/250)+5b = 0.8}}}
{{{-3/10 + 5b = 8/10}}}
{{{5b = 11/10}}}
{{{b = 11/50}}}<br>
ANSWER: The quadratic equation is<br>
{{{y = (-3/250)x^2+(11/50)x+78.2}}}<br>