LESSON 4-2A NOTES: STANDARD FORM OF QUADRATIC FUNCTION
STANDARD FORM:
f(x) = ax2 + bx + c, where a
* The graph of f(x) = ax2 + bx + c, where a
0;
0, is a parabola.
* If a > 0, the parabola opens up. The y-coordinate
of the vertex is the minimum value of the function.
* If a < 0, the parabola opens down. The y-coordinate
of the vertex is the maximum value of the function.
* Axis of Symmetry:
x=
* Vertex: The x-coordinate of the vertex is x =
The y-coordinate of the vertex is the y-value of the function for x =
Vertex = (
, f(
* The y-intercept is (0, c)
, or f(
)
* Range: Use the y-coordinate of the vertex to determine
the range. Minimum: y > Maximum: y <
Examples/Practice 1-4: Identify the vertex, the axis of symmetry, the maximum/minimum value,
the y-intercept, and the range of each function. Then graph each quadratic function in standard
form. Plot the vertex and two other points.
1) y = x2 + 2x + 3
2) y =
2x2 + 2x
5
)
3) y =
x2 + 4x + 1
4) y = 3x2 + 4x
2
Sketch each parabola using the given information.
5) vertex (2, 2), y–intercept 2
6) vertex (2, 5), point (1, 5)