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Identify the vertex and axis of symmetry of the quadratic function.f(x)= - 3(x + 2)^2 + 5

User Shakim
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1 Answer

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We are given the equation of a parabola, and we are asked to find its vertex and axis of symmetry

The general form of a quadratic equation is the following


f(x)=a(x-h)^2+k

Written in this form, the point (h,k) represent the vertex of the parabola, that means that in the equation given by the problem


f(x)=-3(x+2)^2+5

The vertex is the point


(h,k)=(-2,5)

To find the axis of symmetry we need to expand the equation by solving the parenthesis and simplifying


f(x)=-3(x^2+4x+4)+5
f(x)=-3x^2-12x-12+5
f(x)=-3x^2-12x-7

Written in this form, we have that the axis of symmetry is given by


x=-(b)/(2a)

where the coeficient b and a, come from the equation, knowing that the general form is the following


f(x)=ax^2+bx+c

therefor, the axis of symmetry is equal to


x=-(-12)/(2(-3))=-2

User Bandrami
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