a) h(x) = (x + 7)^2 - 9
b) the vertex is at (-7, -9) and it is a minimum.
b) The axis of symmetry is x = -7
How to rewrite the parabola equation?
Here we have the parabola equation:
h(x) = x^2 + 14x + 41
First, we want to rewrite it in vertex form.
We can complete squares first, notice that if we add and subtract 8 we will get:
h(x) = x^2 + 14x + 41 + 8 - 8
h(x) = x^2 + 14x + 49 - 9
h(x) = (x^2 + 2*7*x + 7*7) - 9 = (x + 7)^2 - 9
The parabola in vertex form is:
h(x) = (x + 7)^2 - 9
b) The general vertex form is:
y = (x - h)^2 + k
Where the vertex is (h, k)
Then the vertex of our parabola is (-7, -9)
And because the leading coefficient of our parabola is positive, we can know that the parabola opens upwards, it would mean that the vertex is a minimum.
c) The axis of symmetry is a vertical line such that x is equal to the x-value of the vertex, then the axis of symmetry is:
x = -7.
If you want to learn more about parabolas:
https://brainly.com/question/4061870
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