Question

Find the y-axis of symmetry for this parabola y=-x^2+2x-7

Answer 1

The axis of symmetry of the parabola y = -x² + 2x - 7 is at x = 1

Step-by-step explanation:

In the quadratic equation y = ax² + bx + c, where a, b , c are constant

1. It is represented graphically by a parabola

2. The vertex of the parabola is point (h , k)

3. h = $\frac{-b}{2a}$ and k = f(h), where a is the coefficient of x²

    and b is the coefficient of x

4. The axis of symmetry of the parabola is a vertical line passes through

    the vertex point and its equation is x = h

∵ y = -x² + 2x - 7

∵ y = ax² + bx + c

∴ a = -1 , b = 2 and c = -7

∵ (h , k) are the coordinates of its vertex

∵ h = $\frac{-b}{2a}$

∴ h = $\frac{-2}{2(-1)}$

∴ h = 1

∵ k = f(h)

- Substitute x in the equation by 1

∴ k = -(1)² + 2(1) - 7 = -1 + 2 - 7

∴ k = -6

∴ The coordinates of the vertex of the parabola are (1 , -6)

∵ The axis of symmetry of it is a vertical line passes through the

   vertex point (1 , -6)

∵ Its equation is x = h

∵ h = 1

∴ The equation of the axis of symmetry is x = 1

The axis of symmetry of the parabola y = -x² + 2x - 7 is at x = 1

Learn more:

You can learn more about parabola in brainly.com/question/8054589

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