The graph of a quadratic function is called a parabola. Consider the graph of y = ax^{2} + bx + c, where a is not equal 0.
Notice that using the vertex, y-intercept, and the reflection of the y-intercept, we can roughly graph the quadratic function.
Then, you can always find and graph one or more additional points and their reflection.
Graph x^{2} + 4x - 1
Step 1:
Identify a, b, and c by comparing ax^{2} + bx + c with x^{2} + 4x - 2.
a = 1, b = 4, and c = -1
Step 2:
Find the equation of the axis of symmetry.
x = -4/2 = -2
Step 3:
Find the x-coordinate and y-coordinate of the vertex.
Looking at the graph above, you can see that the vertex is located on the axis of symmetry. Therefore, the x-coordinate of the vertex is x = -2.
To get the y-coordinate, find f(-2)
f(-2) = (-2)^{2} + 4(-2) - 1 = 4 + -8 - 1 = -4 - 1 = -5
Step 4
Find the y-intercept and its reflection.
Since c = -1, the coordinate of the y-intercept is (0, -1).
The coordinate of the y-intercept is located on the right side of the axis of symmetry since 0 is bigger than -2. The y-intercept is 2 units away from the axis of symmetry.
Therefore, the reflection of the y-intercept is also 2 units away from the axis of symmetry. Since the y-intercept is located on the right side of the axis of symmetry, the reflection of the y-intercept is located on the left side of the axis of symmetry. Two units away from -2 and on the left side of -2 is -4, so the coordinate of the reflection of y-intercept is (-4, -1)
Step 5
Graph the vertex (-2, -5), the y-intercept (0,-1) and its reflection (-4,-1), and the axis of symmetry (x = -2). Find some additional points and their reflection and connect the points with a smooth curve.
Jul 03, 20 09:51 AM
factoring trinomials (ax^2 + bx + c ) when a is equal to 1 is the goal of this lesson.
Basic math formulas
Algebra word problems
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.