A pipe that is 3.1 meters long is placed vertically in a pond. Its lowest point is 1.5 meters under the water surface. How far a
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The equation of the line will be given as y = -4x - (- 17/ 4).
<h3>What is an equation?</h3>It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
Given that:-
- The graph of a linear function passes through the points (-1, -1/4) and (1, -3/4).
The equation of the line will be given as:-
y - y₁ = m ( x - x₁)
slope m will be calculated as:-
The equation will be:-
y - (1/4) = -4( x + 1 )
y = -4x - (17/4)
Therefore the equation of the line will be given as y = -4x - (- 17/ 4).
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We are given with a quadratic equation which represents a Parabola , we need to find the vertex of the parabola , But let's recall that , For any quadratic equation of the form ax² + bx + c = 0 , the vertex of the parabola is given by ;
Where , D = b² - 4ac (Discriminant)
Now , On comparing the given equation with ax² + bx + c , we have
⇢⇢⇢ <em><u>a = 1 , b = - 10 , c = 2</u></em><em><u>7</u></em>
Now , Calculating D ;
Now , Calculating the vertex ;
Hence , The vertex of the parabola is at (5,2)
Note :- As the Discriminant < 0 . So , the equation will have imaginary roots .
Refer to the attachment for the graph as well .
