4.1 Graph Quadratic Functions in Standard Form
-Parent Function for Quadratics: f(x)=x2
The shape of a quadratic function is called a _________.
-Vertex: Highest or lowest point on a parabola.
-Axis of symmetry: Divides the parabola into two mirror
images and passes through the vertex.
The equation is a vertical line given by x = the x-coordinate
of the vertex.
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Examples: Graph. Compare the graph with the graph
of y = x2.
1.) y = 2x2
x
-2
-1
0
1
2
y
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2.) y = -½x2 + 3
x
-4
-2
0
2
4
y
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Properties of the graph of y = ax2 + bx + c:
Formula for the x-coordinate of the vertex: x = -b
2a
*Note: This is also the equation of the axis of symmetry.
-The graph opens up if a > 0 and opens down if a < 0.
-If a < 0 , the graph is narrower than y=x2.
-If a > 0 , the graph is wider than y=x2.
-The y-intercept is c. So, the point (0,c) is on the parabola.
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Examples: Graph the function. Label the vertex and
axis of symmetry.
1.) y = 3x2 - 6x + 4
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2.) y = -6x2 - 4x - 5
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3
3.) y = -¾x2-4x-1
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4.1 ICE
Graph the function. Label the vertex and axis of
symmetry.
y = -2x2 + 8x - 1
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