Question

To an equation of a parabola withâ x-intercepts at (one fourth comma 0 ) and (negative 2 comma 0 )which passes through the point (0 comma 2 ).

Answer 1

`y=-4x^2-7x+2`

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

`y=a(x-p)(x-q)`

p=1/4 and q=-2

`y=a(x-(1)/(4))(x-(-2))`

`y=a(x-(1)/(4))(x+2)`

`y=a(x^2+(7x)/(4)-(1)/(2))`

To find out 'a' use the point (0,2)

the value of x=0 and y=2

`2=a(0^2+(7(0))/(4)-(1)/(2))`

a=-4

so equation becomes

`y=-4(x^2+(7x)/(4)-(1)/(2))`

`y=-4x^2-7x+2`