Question #81645
2 Answers
graph{y=x^2-x-6 [-9.96, 10.04, -7.64, 2.36]}
This is the graph of
Explanation:
We can plot a parabola by substituting x=-5 to +5, which will give
24, 14, 6, 0, -4, -6, -6, -4, 0, 14, 24.
By graphing the points, we can link the points to get a parabola.
Note:
Hence, the vertex of the parabola is at
Refer to the explanation.
Explanation:
Graph:
In order to graph a parabola, useful points are the vertex and x-intercepts (if it crosses the x-axis), and other points determined by plugging in different values for
X-intercepts: values of
The given equation is in the factored form of a quadratic equation. We can substitute
Now we need to convert the equation to standard form by FOILing the binomials.
http://www.mathcaptain.com/algebra/foil-method.html
where:
For a quadratic equation in standard form, the
Axis of Symmetry: vertical line that divides the parabola into equal halves
Formula for axis of symmetry for a quadratic equation in standard form:
Vertex: minimum or maximum point on the parabola
Substitute
Other points
First point:
Substitute
Second point:
Substitute
Plot the vertex, x-intercepts, and other points. Sketch a parabola through the points. Do not connect the dots.
graph{y=x^2-x-6 [-10, 10, -5, 5]}