Sketch the graph of the quadratic functions in Exercises 1 and 2, indicating the coordinates of the vertex, the y-intercept, and the x-intercepts (if any).
To graph: The function
Given Information:
The provided function is
Graph:
Consider the function,
Compare the equation
The values are
Here
To graph a quadratic function, four things should be calculated first.
(i) Vertex
(ii) x-intercept
(iii)y-intercept
(iv) Symmetry
Vertex: The formula of x- coordinate of a vertex is,
Substitute
To find the y-coordinate of vertex, substitute
Thus, coordinates of the vertex are
To calculate the x-intercept of the function, substitute
Therefore,
Now solve for
Now solve for
Thus, x-intercept are
To calculate the y-intercept, substitute
Thus, the y-intercept is
Symmetry:
The formula of the symmetry line is,
Substitute
So, the line of symmetry is
Now plot the graph.
Interpretation:
The graph of
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