Answer:
y = 56
Step-by-step explanation:
the midsegment SV is half the length of the side TU , that is
y - 9 = (y + 38) ← multiply both sides by 2 to clear the fraction
2y - 18 = y + 38 ( subtract y from both sides )
y - 18 = 38 ( add 18 to both sides )
y = 56
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 .
