Tutorial Exercise
Use a graphing utility to graph the quadratic function. Identify the vertex, axis of symmetry, and x-intercepts.
f(x) = 2/5(x^2 + 8x - 6)
Check your results algebraically by writing the quadratic function in standard form.
Step 1
Begin by graphing the function using a graphing utility. Locate the vertex, axis of symmetry, and x-intercepts.
We can find the exact answers by writing the equation in standard form. Use the process of completing the square. Begin by moving the constant term outside the parentheses.
f(x) = 2/5(x^2 + 8x) -
Add a constant term inside the parentheses that will allow you to write the resulting trinomial as the square of a binomial. You will need to also subtract the same value outside the parentheses. Include also the constant term from the previous step in the blank provided.
f(x) = 2/5(x^2 + 8x + ) - /5 - 12/5
Write the trinomial as the square of a binomial and simplify the constant term. Give the full equation (Use y for f(x)).
The equation is now in standard form, f(x) = a(x - h)^2 + k.
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