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Identify the vertex first. Then use it to find the axis of symmetry.
x-intercept: x=7
Axis of Symmetry: x=7
Vertex: (7,0)
Graph:
We want to draw the graph of the given quadratic function. To do so, we will rewrite it in vertex form, f(x)=a(x-h)^2+k, where a, h, and k are either positive or negative numbers. y=4(x-7)^2 ⇕ y=4(x-7)^2+0 To draw the graph, we will follow four steps.
Let's get started.
We will first identify the constants a, h, and k. Recall that if a<0, the parabola will open downwards. Conversely, if a>0, the parabola will open upwards. Vertex Form:& f(x)= a(x- h)^2+k Function:& y= 4(x- 7)^2+ We can see that a= 4, h= 7, and k= . Since a is greater than 0, the parabola will open upwards.
Let's now plot the vertex ( h,k) and draw the axis of symmetry x= h. Since we already know the values of h and k, we know that the vertex is ( 7, ). Therefore, the axis of symmetry is the vertical line x= 7.
Note that both points have the same y-coordinate.
Finally, we will sketch the parabola which passes through the three points. Remember not to use a straightedge for this!