Learn Before
Graphing
To graph the parabola , apply the standard graphing procedure using the axis of symmetry, vertex, intercepts, and symmetry.
Identify the coefficients and direction. Here , , and . Because is negative, the parabola opens downward.
Find the axis of symmetry. Use :
The axis of symmetry is the vertical line .
Find the vertex. Substitute into the equation:
The vertex is .
Find the y-intercept. Substitute :
The y-intercept is .
Find the symmetric point. The y-intercept lies 3 units to the left of the axis of symmetry . The point 3 units to the right of the axis is .
Find the x-intercepts. Set and solve:
Factor out :
Recognize the perfect square trinomial:
Solve to get . The only x-intercept is , which is the same as the vertex.
Connect the points , , and with a smooth downward-opening curve.
The vertex and x-intercept coincide because the discriminant of equals zero (), meaning there is exactly one solution and the parabola just touches the x-axis at the vertex.
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Ch.10 Quadratic Equations - Elementary Algebra @ OpenStax
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Learn After
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