Respuesta :
Answer:
(- 1, 0), (9, 0)
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
here (h, k) = (4, 75), so
y = a(x - 4)² + 75
To find a substitute (0, 27) into the equation
27 = a(- 4)² + 75 , that is
27 = 16a + 75 ( subtract 75 from both sides )
16a = - 48 ( divide both sides by 16 )
a = - 3, thus
y = - 3(x - 4)² + 75 ← equation in vertex form
To obtain the x- intercepts let y = 0
- 3(x - 4)² + 75 = 0 ( subtract 75 from both sides )
- 3(x - 4)² = - 75 ( divide both sides by - 3 )
(x - 4)² = 25 ( take the square root of both sides )
x - 4 = ± [tex]\sqrt{25}[/tex] = ± 5
Add 4 to both sides
x = 4 ± 5, hence
x = 4 - 5 = - 1 or x = 4 + 5 = 9
Substitute these values into the equation for corresponding values of y
x = - 1 : y = - 3(- 5)² + 75 = - 75 + 75 = 0 → (- 1, 0)
x = 9 : y = - 3(5)² + 75 = = 75 + 75 = 0 → (9, 0)
The x- intercepts are (- 1, 0), (9, 0)
Answer:
The x intercepts are (-1, 0) and (9, 0).
Step-by-step explanation:
We can write the equation in vertex form:
y = a(x - b)^2 + c
Here b = 4 and c = 75 so we have
y = a(x - 4)^2 + 75 where a is a constant to be found.
The y-intercept is (0,27) so
27 = a(0 - 4)^2 + 75
16a = 27 - 75
a = -48/16 = -3
So to find the x-intercepts we solve the equation:
-3(x - 4)^2 + 75 = 0
(x - 4)^2 = -75 / -3 = 25
x - 4 = +/- √25
x = 5+ 4 = 9 , -5 + 4 = -1.
