The vertex form of a parabola is given by y = a(x-h)² + k, where (h, k) is the vertex of the parabola. Given the vertex (32.5, -137), the equation of the parabola can be written as y = a(x - 32.5)² - 137.

To convert this equation to the standard form y = ax² + bx + c, we expand the equation to get y = ax² - 2ahx + ah² - 137. Comparing this with the standard form, we can see that b = -2ah and c = ah² - 137.

The question asks for the value of a + b + c. Substituting the expressions for b and c, we get a + b + c = a - 2ah + ah² - 137. Since h = 32.5, this simplifies to a - 65a + 1056.25a - 137.

Solving this equation for a, we get a = -137/1056.25 = -0.1297 approximately. Substituting this value into the expressions for b and c, we get b = 2*0.1297*32.5 = 8.41525 and c = 0.1297*1056.25 - 137 = -120.58475.

Therefore, a + b + c = -0.1297 + 8.41525 - 120.58475 = -112.2992. This value is not in the given options, so none of the options could be the value of a + b + c.

Question

The vertex form of a parabola is given by y = a(x-h)² + k, where (h, k) is the vertex of the parabola. Given the vertex (32.5, -137), the equation of the parabola can be written as y = a(x - 32.5)² - 137.

To convert this equation to the standard form y = ax² + bx + c, we expand the equation to get y = ax² - 2ahx + ah² - 137. Comparing this with the standard form, we can see that b = -2ah and c = ah² - 137.

The question asks for the value of a + b + c. Substituting the expressions for b and c, we get a + b + c = a - 2ah + ah² - 137. Since h = 32.5, this simplifies to a - 65a + 1056.25a - 137.

Solving this equation for a, we get a = -137/1056.25 = -0.1297 approximately. Substituting this value into the expressions for b and c, we get b = 2*0.1297*32.5 = 8.41525 and c = 0.1297*1056.25 - 137 = -120.58475.

Therefore, a + b + c = -0.1297 + 8.41525 - 120.58475 = -112.2992. This value is not in the given options, so none of the options could be the value of a + b + c.

Knowee AI · Accepted Answer

The vertex form of a parabola is given by y = a(x-h)² + k, where (h, k) is the vertex of the parabola. Given the vertex (32.5, -137), the equation of the parabola can be written as y = a(x - 32.5)² - 137.

To convert this equation to the standard form y = ax² + bx + c, we expand the equation to get y = ax² - 2ahx + ah² - 137. Comparing this with the standard form, we can see that b = -2ah and c = ah² - 137.

The question asks for the value of a + b + c. Substituting the expressions for b and c, we get a + b + c = a - 2ah + ah² - 137. Since h = 32.5, this simplifies to a - 65a + 1056.25a - 137.

Solving this equation for a, we get a = -137/1056.25 = -0.1297 approximately. Substituting this value into the expressions for b and c, we get b = 2*0.1297*32.5 = 8.41525 and c = 0.1297*1056.25 - 137 = -120.58475.

Therefore, a + b + c = -0.1297 + 8.41525 - 120.58475 = -112.2992. This value is not in the given options, so none of the options could be the value of a + b + c.

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