McGraw Hill Glencoe Algebra 2, 2012
MH
McGraw Hill Glencoe Algebra 2, 2012 View details
7. Transformations of Quadratic Graphs
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Exercise 50 Page 279

Expand the vertex form of the quadratic.

Equation:
Vertex:
Axis of Symmetry:

Practice makes perfect
Let's look at the two forms of the quadratic.
We are asked to express and in terms of and Let's expand the Vertex Form.
Compare the coefficients of this expanded form to the coefficients of the standard form.
  • The coefficient of the quadratic term is in both forms.
  • The coefficients of the linear terms should be the same. This allows us to write an equation and solve it for
Solve for
  • The constant terms of the two forms must also be the same. Using the expression for we just found, this allows us to find an expression for
Solve for
Using the expressions we found, we can write the vertex form using the coefficients of the standard form. We can also simplify the result.
Using that the vertex is on the vertical axis of symmetry, our calculation also gives the answer to the second part of the question.