Write the formula for the parabola that has x-intercepts (−2,0) and (4.6,0), and y-intercept (0,1.5)
in my answer i put 0 instead of x and 1.5 instead of y I am so sorry the answer should be y=(-1.5/9.2)(x+2)(x-4.6) not 1.5=(-1.5/9.2)(0+2)(0-4.6)
y=(-1.5/9.2)(x+2)(x-4.6)
parabola x intercept form is:
y=a(x-x1)(x-x2)
x1 and x2 being the x intercepts
x intercepts are -2 and 4.6
-(-2)=2
-(4.6)=4.6
therefore
y=a(x+2)(x-4.6)
to solve for a substitute with the other coordinate they give you (0,1.5)
1.5=a(0+2)(0-4.6)
1.5=a*2*-4.6
1.5= -9.2a
1.5/-9.2 = a
-1.5/9.2 = a
answer: 1.5=(-1.5/9.2)(0+2)(0-4.6)
hope this helps :)
The answer should be:
y=(-1.5/9.2)(x^2 - 2.6 - 9.2)
The correct answer is y=(-1.5/9.2)(x^2 - 2.6 - 9.2)
To write the formula for a parabola, we need to start with the standard form of the equation:
y = a(x - h)^2 + k
where (h, k) is the vertex of the parabola, and a determines the shape and direction of the parabola.
Given that the parabola has x-intercepts at (-2, 0) and (4.6, 0), we can deduce that the vertex lies between these two x-intercepts. To find the x-coordinate of the vertex, we calculate the average of the x-intercepts:
h = (-2 + 4.6) / 2
h = 2.6 / 2
h = 1.3
Since the vertex lies on the line of symmetry, it means h = 1.3.
The y-intercept is given as (0, 1.5), which gives us the value of k. Therefore, k = 1.5.
Now we have h = 1.3 and k = 1.5. To find a, we can substitute these values and one of the x-intercepts into the equation and solve for a.
Using the point (-2, 0), we have:
0 = a(-2 - 1.3)^2 + 1.5
Solving this equation will give us the value of a.
0 = a(-3.3)^2 + 1.5
0 = 10.89a + 1.5
10.89a = -1.5
a = -1.5 / 10.89
a ≈ -0.138
Now that we have the values for a, h, and k, we can write the equation of the parabola:
y = -0.138(x - 1.3)^2 + 1.5
So, the formula for the parabola is y = -0.138(x - 1.3)^2 + 1.5.
Note: The given x-int. satisfy my Eq., but my y-int. is -9.2 instead of 1.5.
To start, what is the generic formula for a parabola?
given the roots,
y = a(x+2.0)(x-4.6)
Now plug in the point (0,1.5) and you get
a(0+2.0)(0-4.6) = 1.5
-9.2a = 1.5
a = -1.5/9.2 ≈ -0.16
That means
y = -0.16(x+2.0)(x-4.6)
You can massage that into whatever form you need.
Y = Ax^2 + Bx + C.
C = -4.6 * 2 = -9.2.
B = -4.6 + 2 = -2.6.
h = (-2 + 4.6)/2 = 1.3.
h = -B/2A = 1.3.
2.6/2A = 1.3,
A = 1.
Eq: Y = x^2 - 2.6x - 9.2.