A Parabola has a vertex (-3,7) and one x intercept is -11. Find the other x intercept and the y intercept. How on earth do i do this
(-11, 0), V(-3, 7), (x, 0).
The x-intercepts are the same distance from the axis of symmetry.
Therefore, -3-(-11) = x - (-3).
8 = x + 3,
X = 5. = The 2nd x-int.
Y = a(x-h)^2 + k.
Y = a(x+3)^2 + 7,
0 = a(5+3)^2+ 7,
a = -7/64.
Eq: Y = -7/64(x+3)^2 + 7. X = 0 at Y-int.
Y-int. = -7/64(0+3)^2 +7 = -7/64 * 9 + 7 = -63/64 + 7 = 385/64. = 6.0
Im not sure you did it right on my book it said y=385/64 but the X intercepts were right.
385/64 is correct. Just plug in x=0 to get that.
ok At y-7 = -7/64 (x+3)^2
where did you get -55 from
y = -7/64 (x^2 + 6x - 55)
@Oobleck please answer
oh come on
y-7 = -7/64 (x+3)^2
y = -7/64 (x^2+6x+9) + 7*64/64
y = -7/64 (x^2+6x+9-64)
y = -7/64 (x^2+6x-55)
To find the other x-intercept and the y-intercept of a parabola with the given information, you can use the vertex form of a parabola equation.
The vertex form of a parabola equation is given by:
y = a(x - h)^2 + k
Where:
- (h, k) represents the coordinates of the vertex, in this case (-3, 7).
- a is the coefficient that determines the shape and direction of the parabola.
Since the parabola has a vertex at (-3, 7) and one x-intercept at -11, we can use this information to find the value of 'a' in the vertex form equation.
Step 1: Determine the value of 'a' using the vertex and the x-intercept.
To find 'a', substitute the given values of a point (-11, 0) (the x-intercept) into the equation and solve for 'a'.
0 = a(-11 - (-3))^2 + 7
Simplifying the equation, we get:
0 = a(-11 + 3)^2 + 7
0 = a(-8)^2 + 7
0 = 64a + 7
Now solve for 'a':
64a = -7
a = -7/64
Step 2: Substitute 'a' into the vertex form equation.
Now that we know the value of 'a', we can rewrite the equation using the vertex form:
y = (-7/64)(x - (-3))^2 + 7
y = (-7/64)(x + 3)^2 + 7
Step 3: Find the other x-intercept.
To find the other x-intercept, set y equal to 0 in the equation and solve for 'x'.
0 = (-7/64)(x + 3)^2 + 7
Rearranging the equation, we get:
(-7/64)(x + 3)^2 = -7
Divide both sides by (-7/64):
(x + 3)^2 = 1
Taking the square root of both sides:
x + 3 = ±1
Solving for 'x':
x = -3 ± 1
Therefore, the other x-intercepts are:
x = -3 + 1 = -2
x = -3 - 1 = -4
So, the x-intercepts are x = -11, x = -2, and x = -4.
Step 4: Find the y-intercept.
To find the y-intercept, we substitute x = 0 into the equation and solve for 'y':
y = (-7/64)(0 + 3)^2 + 7
y = (-7/64)(3^2) + 7
y = (-7/64)(9) + 7
y = -63/64 + 7
y = -63/64 + (7*64)/64
y = -63/64 + 448/64
y = 385/64
Therefore, the y-intercept is y = 385/64.
In summary:
The other x-intercepts are x = -2 and x = -4, while the y-intercept is y = 385/64.
X = -11 X = 5 Y = 385/64
since the vertex is at (-3,7), the equation is
y-7 = a(x+3)^2
Since the point (-11,0) is on the graph, we have
0-7 = a(-11+3)^2
-7 = 64a
a = -7/64
so, the equation is
y-7 = -7/64 (x+3)^2
In the more usual form, that is
y = -7/64 (x^2 + 6x - 55)
or
y = -7/64 (x+11)(x-5)
so, what do you think?