The equation of the parabola is .
Further explanation:
The equation of parabola in form of quadratic equation is as follows:
The given points are shown below in Table 1.
Step 1:
The parabola passes through point , it can be written as follows:
Step 2:
The parabola passes through point , it can be written as follows:
Step 3:
The parabola passes through point , it can be written as follows:
From step 2, substitute for in equation (1).
From step 2, substitute -6 for in equation (2).
Subtract equation (3) from equation (4).
Substitute 5 for in equation (3) to obtain the value of .
Substitute 4 for , 5 for and for in equation to obtain the equation of the parabola.
The graph of the parabola is shown below in figure 1.
Thus, the equation of the parabola is .
Learn more:
1. Which function has an inverse that is also a function? {(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)} {(–1, 2), (0, 4), (1, 5), (5, 4), (7, 2)} {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} {(–1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}
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2. A given line has the equation 10x + 2y = −2. what is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)? y = ( )x + 12
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3. what are the domain and range of the function f(x) = 3x + 5?
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Answer Details :
Grade: High School.
Subject: Mathematics.
Chapter: Coordinate geometry.
Keywords:
Parabola, standard form of the parabola, y=ax^2+bx+c, quadratic equation, vertex of the parabola, y=4x^2+5x-6, intervals, intercepts, function value, intercepts of lines, slope, slope intercept form, continuous, range, point.