What is the standard form of the equation of the parabola that has a vertex at (4, 3) and passes through the point (-4, -2)?
Is it f(x) = -5/64(x - 4)^2 + 3?
let's test it.
does (-4,-2) satisfy your equation ?
LS = -2
RS = (-5/6)(64) + 3 ≠ -2
Nope!
Looks like you had a good part of it.
the equation must be
y = a(x-4)^2 + 3
plug in (-4,-2)
-2 = a(64) +3
take over, let me know what you got
The equation -2 = a(64) +3 gives 64a = -5, or a = -5/64.
To determine if the equation you provided is the correct standard form of the equation of the parabola, we can follow these steps:
Step 1: Understand the standard form of the equation of a parabola.
The standard form of the equation for a parabola is y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola.
Step 2: Use the given information to determine the values of h and k.
In the given equation, the vertex is (4, 3), so h = 4 and k = 3.
Step 3: Plug in the vertex values to form the equation.
Using the vertex values, we can rewrite the equation as y = a(x - 4)^2 + 3.
Step 4: Use the point (-4, -2) to find the value of a.
The equation passes through the point (-4, -2), meaning that when x = -4, y = -2. Plugging these values into the equation, we get -2 = a(-4 - 4)^2 + 3.
Simplifying this equation, we have -2 = a(-8)^2 + 3, which further simplifies to -2 = 64a + 3.
Step 5: Solve for a.
Subtracting 3 from both sides of the equation, we have -2 - 3 = 64a, which simplifies to -5 = 64a.
To isolate a, we divide both sides of the equation by 64, giving us a = -5/64.
Step 6: Substitute the value of a back into the equation.
Now that we know the value of a, we can substitute it back into the equation y = a(x - 4)^2 + 3.
Therefore, the correct equation for the parabola with a vertex at (4, 3) and passing through the point (-4, -2) is y = (-5/64)(x - 4)^2 + 3.
So, yes, f(x) = -5/64(x - 4)^2 + 3 is the correct standard form of the equation for the given parabola.