Answer:
[tex]y=-4x^2-7x+2[/tex]
Step-by-step explanation:
an equation of a parabola withâ x-intercepts at (1/4, 0 ) and (-2,0 )which passes through the point (0,2 )
the equation of the parabola with x intercepts in factored form is
[tex]y=a(x-p)(x-q)[/tex]
p=1/4 and q=-2
[tex]y=a(x-\frac{1}{4})(x-(-2))[/tex]
[tex]y=a(x-\frac{1}{4})(x+2)[/tex]
[tex]y=a(x^2+\frac{7x}{4}-\frac{1}{2})[/tex]
To find out 'a' use the point (0,2)
the value of x=0 and y=2
[tex]2=a(0^2+\frac{7(0)}{4}-\frac{1}{2})[/tex]
a=-4
so equation becomes
[tex]y=-4(x^2+\frac{7x}{4}-\frac{1}{2})[/tex]
[tex]y=-4x^2-7x+2[/tex]
