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Write the parabola s equation in graphing form, and identify its vertex. Also, determine the locations of its roots and sketch its graph. (1) (2) GRAPHING FORM: GRAPHING FORM: VERTEX: VERTEX: ROOTS:
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How to write the parabola's equation:
01
First, identify the vertex of the parabola. This can be done by finding the x-coordinate of the vertex using the formula x = -b / (2a), where a and b are coefficients in the standard form equation of a parabola, y = ax^2 + bx + c.
02
Next, determine whether the parabola opens upwards or downwards. If the coefficient a is positive, the parabola opens upwards, and if it is negative, the parabola opens downwards.
03
Then, find the y-coordinate of the vertex by plugging the x-coordinate from step 1 into the equation of the parabola.
04
Now, you have the vertex, which is in the format (h, k), where h is the x-coordinate and k is the y-coordinate.
05
To write the equation of the parabola, replace the values of h and k in the standard form equation. The equation will be of the form y = a(x - h)^2 + k, where (x, y) represents any point on the parabola.
06
Finally, simplify the equation if needed and provide the appropriate values for a, h, and k.
Who needs to write the parabola's equation:
01
Mathematics students who are studying conic sections and specifically need to analyze or graph quadratic functions often need to write the parabola's equation.
02
Engineers and architects who design structures, such as bridges or arches, may need to write the parabola's equation to understand the shape and properties of their designs.
03
Physicists who study projectile motion or the motion of objects under the influence of gravity may need to write the parabola's equation to describe the path followed by the object.
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What is write the parabola39s equation?
The general form of a parabola's equation is y = ax^2 + bx + c.
Who is required to file write the parabola39s equation?
Students studying mathematics and physics may be required to write the parabola's equation.
How to fill out write the parabola39s equation?
To fill out the parabola's equation, substitute the values of a, b, and c into the equation y = ax^2 + bx + c.
What is the purpose of write the parabola39s equation?
The purpose of writing the parabola's equation is to represent the shape of a parabolic curve and analyze its properties.
What information must be reported on write the parabola39s equation?
The information required to write the parabola's equation includes the coefficients a, b, and c that determine the specific form of the parabola.
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