Explanation:
The equation of a parabola has the following form:
f(x) = ax² + bx + c
Where a, b, and c are constant values.
If a is positive, the parabola opens up and if a is negative the parabola opens down. Additionally, the value of c is the y-intercept of the parabola, it is the point where the graph crosses the y-axis.
Therefore, if the equation of the parabola is:
f(x) = -x² + x - 5
We get that a = -1, b = 1, and c = -5
Then, since a is negative, the parabola opens down and since c is -5, the y-intercept of the parabola is -5.
Finally, the x-coordinate of the vertex of a parabola can be calculated as:
[tex]x-\text{coordinate = }\frac{-b}{2a}=\frac{-1}{2(-1)}=\frac{-1}{-2}=0.5[/tex]So, the y coordinate can be calculated as:
[tex]\begin{gathered} f(x)=-x^2+x-5 \\ f(x)=-0.5^2+0.5-5 \\ f(x)=-4.75 \end{gathered}[/tex]Then, the vertex of the parabola is the point (0.5, -4.75)
RT
