Answer:
(D)y=-5x²+20x+25
Explanation:
The parabola intersects the x-axis at the points -1 and 5. Therefore:
[tex]\begin{gathered} x=-1\; or\; x=5 \\ (x-(-1))(x-5)=0 \\ (x+1)(x-5)=0 \\ x^2-5x+x-5=0 \\ x^2-4x-5=0 \end{gathered}[/tex]
Since the parabola is an upward-facing parabola, the coefficient of x² must be a negative number. Therefore, we multiply all through by a minus sign to have:
[tex]0=-x^2+4x+5[/tex]
To obtain a form similar to the given options, we multiply the right-hand side by 5.
[tex]y=-5x^2+20x+25[/tex]
The correct choice is D.
