Find the value of a and b if the parabola y = x ^ 2 + ax + b passes through points A (1; 2) and B (4; 2).
May 31, 2021 | education
| Find a and b.
The parabola of the function y = x ^ 2 + a * x + b passes through the points A (1; 2) and B (4; 2).
Let’s compose a system of equations.
{2 = 1 ^ 2 + a * 1 + b;
2 = 4 ^ 2 + a * 4 + b;
{2 = 1 + a + b;
2 = 16 + 4 * a + b;
{a + b + 1 = 2;
4 * a + b + 16 = 2;
Let us express b from the first equation.
{b = 2 – 1 – a;
4 * a + b = 2 – 16;
{b = 1 – a;
4 * a + b = -14;
Let’s substitute in the second equation.
{b = 1 – a;
4 * a + 1 – a = -14;
{b = 1 – a;
3 * a + 1 = -14;
{b = 1 – a;
3 * a = -14 – 1;
{b = 1 – a;
3 * a = -15;
{b = 1 – a;
a = -15/3;
{b = 1 – a;
a = -5;
{b = 1 – (-5);
a = -5;
{a = -5;
b = 1 + 5;
{a = -5;
b = 6.
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