How do you find the slope of the parabola y=ax2+bx+c, where a, b, c, are constants?
Answers
Answer:
Step-by-step explanation:
A nonlinear function that can be written on the standard form
ax2+bx+c,wherea≠0
is called a quadratic function.
All quadratic functions has a U-shaped graph called a parabola. The parent quadratic function is
y=x2
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The lowest or the highest point on a parabola is called the vertex. The vertex has the x-coordinate
x=−b2a
The y-coordinate of the vertex is the maximum or minimum value of the function.
a > 0 parabola opens up minimum value
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a < 0 parabola opens down maximum value
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A rule of thumb reminds us that when we have a positive symbol before x2 we get a happy expression on the graph and a negative symbol renders a sad expression.
The vertical line that passes through the vertex and divides the parabola in two is called the axis of symmetry. The axis of symmetry has the equation
x=−b2a
The y-intercept of the equation is c.
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When you want to graph a quadratic function you begin by making a table of values for some values of your function and then plot those values in a coordinate plane and draw a smooth curve through the points.