Converting quadratic functions Enter your quadratic function here. Instead of x�, you can also write x^2. Get the following form: Vertex form Normal form Factorized form
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Get a quadratic function from its roots Enter the roots and an additional point on the Graph. Mathepower finds the function and sketches the parabola. Roots at and Further point on the Graph: P(|)
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Calculate a quadratic function given the vertex point Enter the vertex point and another point on the graph. Vertex point: (|) Further point: (|)
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Computing a quadratic function out of three points Enter three points. Mathepower calculates the quadratic function whose graph goes through those points. Point A(|) Point B(|) Point C(|)
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Find the roots Enter the function whose roots you want to find. Hints: Enter as 3*x^2 , as (x+1)/(x-2x^4) and
as 3/5.
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Transforming functions Enter your function here.
How shall your function be transformed? By in x-direction By in y-direction By to the By to the
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Find a function Degree of the function:
( The degree is the highest power of an x. ) Symmetries: axis symmetric to the y-axis point symmetric to the origin y-axis intercept
Roots / Maxima / Minima /Inflection points: at x= at x= at x= at x= at x= Characteristic points: at |) at |) at |) at (|) at (|)
Slope at given x-coordinates: Slope at x= Slope at x= Slope at
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What are quadratic functions?
Quadratic functions are functions of the form . This means, there is no x to a higher power than . The graph of a quadratic function is a
parabola.
The graph of a quadratic function is a parabola. The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves. The axis of symmetry always passes through the vertex of the parabola . The x
-coordinate of the vertex is the equation of the axis of symmetry of the parabola.
For a quadratic function in standard form, y = a x 2 + b x + c , the axis of symmetry is a vertical line x
= − b 2 a .
Example 1:
Find the axis of symmetry of the parabola shown.
The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola.
The vertex of the parabola is
( 2 , 1 ) .
So, the axis of symmetry is the line x = 2 .
Example 2:
Find the axis of symmetry of the graph of y = x 2 − 6 x + 5 using the formula.
For a quadratic function in standard
form, y = a x 2 + b x + c , the axis of symmetry is a vertical line x = − b 2 a .
Here, a = 1 , b = − 6 and c = 5
.
Substitute.
x = − − 6 2 ( 1 )
Simplify.
x = 6 2 = 3
Therefore, the
axis of symmetry is x = 3 .
How do you find the equation of the axis of symmetry?
The axis of symmetry always passes through the vertex of the parabola . The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola. For a quadratic function in standard form, y=ax2+bx+c , the axis of symmetry is a vertical line x=−b2a .
How do you find the equation of the vertex and axis of symmetry?
The Vertex Form of a quadratic function is given by: f(x)=a(x−h)2+k , where (h,k) is the Vertex of the parabola. x=h is the axis of symmetry. Use completing the square method to convert f(x) into Vertex Form.