# 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).

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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