How do you find the axis of symmetry, vertex and x intercepts for #y=-3x^2+6x+1#?
2 Answers
Explanation:
To find the vertex and axis of symmetry:
Put the equation in standard form:
First factor the
Use completing of the square:
1. Multiply the
2. Write the completed square:
3. Add the
4. Notice from step 3, an extra constant was added when completing the square:
5.
To find
Use the quadratic equation since factoring isn't simple. Put the equation in the form:
Please see the explanation.
Explanation:
When given a quadratic of the form:
The equation for axis of symmetry is:
The x coordinate of the vertex, h, is the same as the axis of symmetry:
The y coordinate of the vertex, k, is the function evaluated at h:
The x intercepts can be found by factoring or by using the quadratic formula:
Now, to the given equation:
Please observe that
The computation for the axis of symmetry is as follows:
The x coordinate of the vertex, h, is the same as the axis of symmetry:
The y coordinate of the vertex, k, is the function evaluated at h:
The vertex is the point
As a prelude to finding the x intercepts, compute
Because 48 is a positive real number, we know that there are two distinct roots and, because 48 is not a perfect square, we know that the quadratic will not factor.
Therefore, we find x intercepts using the quadratic formula: