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y=2x^(2)-6x-5 (Use decimals in your answers.) Axis of symmetry: ◻ Vertex: ◻

y=2x2−6x−5 y=2 x^{2}-6 x-5 (Use decimals in your answers.)\newlineAxis of symmetry: □ \square \newlineVertex: □ \square

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Convert equations of parabolas from general to vertex formright chevron icon

Full solution

Q. y=2x2−6x−5 y=2 x^{2}-6 x-5 (Use decimals in your answers.)\newlineAxis of symmetry: □ \square \newlineVertex: □ \square
  1. Identify Coefficients: Identify the coefficients from the quadratic equation y=2x2−6x−5y = 2x^2 - 6x - 5 for use in formulas. Coefficients are: a=2a = 2, b=−6b = -6, and c=−5c = -5.
  2. Calculate Axis of Symmetry: Calculate the axis of symmetry using the formula x=−b2ax = -\frac{b}{2a}. Here, x=−(−6)2⋅2=64=1.5x = -\frac{(-6)}{2\cdot 2} = \frac{6}{4} = 1.5.
  3. Substitute x=1.5x = 1.5: Substitute x=1.5x = 1.5 back into the original equation to find the y-coordinate of the vertex. y=2(1.5)2−6(1.5)−5=2(2.25)−9−5=4.5−9−5=−9.5y = 2(1.5)^2 - 6(1.5) - 5 = 2(2.25) - 9 - 5 = 4.5 - 9 - 5 = -9.5.

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