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

1 Answer
May 20, 2017

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

Explanation:

The axis of symmetry is given by $x = - \frac{b}{2 a}$ for any quadratic of the form $y = a {x}^{2} + b x + c$.

Therefore, the axis of symmetry is:

$x = - \frac{- 8}{2 \left(- 1\right)} = - 4$.

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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.

$y = - {x}^{2} - 8 x + 10$
$y = - {\left(- 4\right)}^{2} - 8 \left(- 4\right) + 10$
$y = - 16 + 32 + 10$
$y = 26$

Final Answer