# how to graph quadatic function. name the vertex, equation of the line of symmetry and the minimum/maximum value.no

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### 1 Answer

(1) Given standard form: `f(x)=ax^2+bx+c`

(a) The vertex will be at `(-b/(2a),f(-b/(2a)))`

(b) The axis of symmetry is `x=-b/(2a)`

(c) If a>0, the vertex is the minimum. If a<0 the vertex is the maximum.

(2) Given vertex form: `f(x)=a(x-h)^2+k`

(a) The vertex is at (h,k).

(b) The axis of symmetry is x=h.

(c) If a>0, the vertex is a minimum, if a<0 the vertex is a maximum.

(3) Given intercept form: f(x)=a(x-p)(x-q)

(a) The vertex is at `((p+q)/2,f((p+q)/2))`

(b) The axis of symmetry is `x=(p+q)/2`

(c) If a>0 the vertex is a minimum, if a<0 the vertex is a maximum.

(4) In any other form, convert to one of these forms.

In all cases to graph: plot the vertex. If a>0, the graph is a parabola (u shape) opening up; if a<0 it opens down. Find at least two more points on the same side of the vertex. Each of these points will have a "mirror" point across the line of symmetry giving you 5 points to draw a smooth curve through.