How do find the vertex and axis of symmetry, and intercepts for a quadratic equation #y= x^2 + 6x + 5#?
Axis of Symmetry is at :
The Vertex Form of a quadratic function is given by:
Use completing the square method to convert
Consider the quadratic
Step 1 - Move the constant value to the right-hand side.
Subtract 5 from both sides.
Step 2 - Add a value to both sides.
What value to add?
Add the square of
Step 3 - Write as Perfect Square.
Now, we have the vertex form.
Hence, Vertex is at
Axis of Symmetry is at
Step 4 - Write the x, y intercepts.
To find the solutions, take square root on both sides.
There are two solutions.
Hence, we have two x-intercepts:
To find the y-intercept:
Hence, y-intercept is at
Analyze the image of the graph below: