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

Answer:

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

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

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

p=1/4 and q=-2

$y=a(x-\frac{1}{4})(x-(-2))$

$y=a(x-\frac{1}{4})(x+2)$

$y=a(x^2+\frac{7x}{4}-\frac{1}{2})$

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

the value of x=0 and y=2

$2=a(0^2+\frac{7(0)}{4}-\frac{1}{2})$

a=-4

so equation becomes

$y=-4(x^2+\frac{7x}{4}-\frac{1}{2})$

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