How do you find the axis of symmetry and vertex point of the function: #y= -x^2-4x+5#?

Answer 1

The axis of symmetry is #x=-2#.
The vertex is #(-2,9)#.

#y=-x^2-4x+5# is a quadratic equation in the form #y=ax+bx+c#, where #a=-1, b=-4, and c=5#.
Axis of Symmetry An imaginary vertical line that divides the parabola into two equal halves. The formula for determining the axis of symmetry is #x=(-b)/(2a)#
#x=(-(-4))/((2*-1))=4/(-2)=-2#
The axis of symmetry is #x=-2#
Vertex The maximum or minimum point of the parabola. Since #a# is a negative number, this parabola opens downward and the vertex is the maximum point.
The #x# value for the vertex is the same as the axis of symmetry. To find the #y# value, substitute #-2# for #x# in the equation. Solve for #y#.
#y=-x^2-4x+5#
#y=-(-2)^2-4(-2)+5=#
#y=-4+8+5=9#
The vertex is #(-2,9)#.

graph{y=-x^2-4x+5 [-14.95, 13.52, -3.76, 10.48]}

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Answer 2

To find the axis of symmetry of a quadratic function in the form y = ax^2 + bx + c, you use the formula x = -b / (2a). For the given function y = -x^2 - 4x + 5, a = -1 and b = -4. Substituting these values into the formula, we get x = -(-4) / (2 * -1) = 4 / -2 = -2. So, the axis of symmetry is x = -2. To find the vertex point, substitute the value of x = -2 into the original function: y = -(-2)^2 - 4(-2) + 5 = -4 + 8 + 5 = 9. So, the vertex point is (-2, 9).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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