Find the vertex of the parabola given by the equation (y = 2x^2 + 8x + 7)

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Accepted Answer

Step:1 ：The general form of a parabola is (y = ax^2 + bx + c ). To find the vertex ((h, k)), we can use the formula (h = -frac{b}{2a}) and (k = c - frac{b^2}{4a}).Step:2 ：Substitute (a = 2), (b = 8), and (c = 7) into the formulas. The x-coordinate of the vertex is (h = -frac{8}{2 times 2} = -1).Step:3 ：Substitute (h = -1) into the equation to get the y-coordinate of the vertex. The y-coordinate is (k = 2(-1)^2 + 8(-1) + 7 = -3).

Answer

Step: 1 ：The general form of a parabola is (y = ax^2 + bx + c ). To find the vertex ((h, k)), we can use the formula (h = -frac{b}{2a}) and (k = c - frac{b^2}{4a}).Step: 2 ：Substitute (a = 2), (b = 8), and (c = 7) into the formulas. The x-coordinate of the vertex is (h = -frac{8}{2 times 2} = -1).Step: 3 ：Substitute (h = -1) into the equation to get the y-coordinate of the vertex. The y-coordinate is (k = 2(-1)^2 + 8(-1) + 7 = -3).

Find the vertex of the parabola given by the equation \(y = 2x^2 + 8x + 7\)

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