Given the quadratic function (y = ax^2 + bx + c) passes through the points (1,7), (2,11), (3,17), determine the constant of variation (a).

Question

Accepted Answer

Step:1 ：Step 1: Substituting the values from the points into the quadratic function gives us the following system of equations: [begin{align*} a + b + c &= 7, quad (1)  4a + 2b + c &= 11, quad (2)  9a + 3b + c &= 17. quad (3) end{align*}]Step:2 ：Step 2: Subtract equation (1) from equations (2) and (3). This will give us: [begin{align*} 3a + b &= 4, quad (4)  8a + 2b &= 10. quad (5) end{align*}]Step:3 ：Step 3: Subtract equation (4) from equation (5). This will give us: [5a = 6]Step:4 ：Step 4: Solve for (a): [a = frac{6}{5}]

Answer

Step: 1 ：Step 1: Substituting the values from the points into the quadratic function gives us the following system of equations: [begin{align*} a + b + c &= 7, quad (1)  4a + 2b + c &= 11, quad (2)  9a + 3b + c &= 17. quad (3) end{align*}]Step: 2 ：Step 2: Subtract equation (1) from equations (2) and (3). This will give us: [begin{align*} 3a + b &= 4, quad (4)  8a + 2b &= 10. quad (5) end{align*}]Step: 3 ：Step 3: Subtract equation (4) from equation (5). This will give us: [5a = 6]Step: 4 ：Step 4: Solve for (a): [a = frac{6}{5}]

Given the quadratic function $y = a x^{2} + b x + c$ passes through the points (1,7), (2,11), (3,17), determine the constant of variation $a$ .

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Popular Problems

Given the quadratic function y=ax2+bx+c passes through the points (1,7), (2,11), (3,17), determine the constant of variation a.

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Popular Problems

Given the quadratic function $y = a x^{2} + b x + c$ passes through the points (1,7), (2,11), (3,17), determine the constant of variation $a$ .