Respuesta :
Answer: The answer is [tex]15y+4=25(x-1.6)^2.[/tex]
Step-by-step explanation: We are to find the equation of the parabola with x-intercepts (-2,0), (1.2,0) and y-intercept (0,-4).
Therefore, axis of symmetry is
[tex]x=\dfrac{1.2+2}{2}\\\\\Rightarrow x=1.6.[/tex]
Let the equation of the parabola be [tex]y=a(x-1.6)^2+k.[/tex]
Substituting the points (x,y)=(0,-4) and (1.2,0) in the above equation, we find that
[tex]-4=a(0-1.6)^2+k\\\\\Rightarrow k=-2.56a-4[/tex]
and
[tex]0=a(1.2-1.6)^2+k\\\\\Rightarrow k=-0.16a.[/tex]
Solving the above two equations, we get
[tex]a=-\dfrac{5}{3}~~\textup{and}~~k=-\dfrac{4}{15}.[/tex]
So, putting the values of 'a' and 'k' in the equation of the parabola, we get
[tex]y=-\dfrac{5}{3}(x-1.6)^2-\dfrac{4}{15}\\\\\Rightarrow 15y+4=-25(x-1.6)^2.[/tex]
Thus, the equation of the parabola is [tex]15y+4=25(x-1.6)^2.[/tex]
Answer:
PLEASE MARK BRAINLIEST
Step-by-step explanation:
x− intercepts (−2,0) and (1.2,0) means that
y = a(x+2)(5x-6)
Now plug in (0,-4) to find a:
a(2)(-6) = -4
-12a = -4
a = 1/3
y = 1/3 (x+2)(5x-6) = 1/3 (5x^2 + 4x - 12)
