Write a quadratic function that represents a parabola that opens upward and has x-intercepts (-8,0) and (-1,0)
1 answer:
The x intercepts give a clue to find the equation. We know that factored quadratic equations are written in the form (x+n)(x+n)=0, where n is a positive or negative number. This means that when you solve for x, you must handle each bracket individually, like this:
x+n=0
x=-n
This gives us the x intercept of (-n, 0)
Using this example, we notice that the coordinate of x on the x intercept is the opposite of the number in the parentheses. So, the factored form of an equation going through the x intercepts (-8,0) and (-1,0) is (x+8)(x+1). Now, we just expand the brackets to give us the full equation:
x+n=0
x=-n
This gives us the x intercept of (-n, 0)
Using this example, we notice that the coordinate of x on the x intercept is the opposite of the number in the parentheses. So, the factored form of an equation going through the x intercepts (-8,0) and (-1,0) is (x+8)(x+1). Now, we just expand the brackets to give us the full equation:
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Answer:
True
Step-by-step explanation:
<u><em>Explanation</em></u>:-
The equation of the standard hyperbola is
- Center is (0,0)
- Hyperbola is symmetric with respective to both the axes, since if (x, y) is a point on the hyperbola, then (-x, y), (-x,-y), (x,-y) are also lie on the parabola.
- The relation of between focus and transverse and conjugate axes c²=a²+b²
- The transverse axis is along x-axis
- The conjugate axis is along y-axis
- The length of transverse axis is 2 a
- The length of conjugate axis is 2 b
- The foci is (±c,0) and the equation of foci is x=±a e)
- The length of Latus rectum is
