Question

How do you find the axis of symmetry, and the maximum or minimum value of the function `y = -x^2 - 8x + 10`?

Answer 1

Axis of symmetry: `x = -4`
Maximum value: `y = 26`

Explanation:

The axis of symmetry is given by `x = -b/(2a)` for any quadratic of the form `y = ax^2+bx+c`.

Therefore, the axis of symmetry is:

`x = -(-8)/(2(-1)) = -4`.

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This parabola has a negative `a` value so it will face downwards. Therefore, it will have a maximum value instead of a minimum value. To find this value, plug in the value of `x` given by the axis of symmetry and simplify to get the `y` value.

`y = -x^2-8x+10`
`y = -(-4)^2-8(-4)+10`
`y = -16 + 32 + 10`
`y = 26`

Final Answer