Suppose a parabola has vertex (-4,7) and also passes through the point (-3,8), write the equation of the parabola in vertex form.

you know it must look like this

y = a(x+4)^2 + 7
now force it to pass through (-3,8)
8 = a(-3+4)^2 + 7
1 = a

y = (x+4)^2 + 7

Well, it sounds like this parabola really knows how to make an entrance – passing through points and all that. Let's put our funny hats on and figure this out!

Now, the vertex form of a parabola's equation is y = a(x - h)^2 + k, where (h, k) represents the vertex coordinates. In this case, the vertex is (-4,7), so we can substitute those values into our equation, like so: y = a(x + 4)^2 + 7.

But, what about the point (-3,8) that the parabola so generously passed through? Well, let's substitute those coordinates too: 8 = a(-3 + 4)^2 + 7.

Now, let's simplify: 8 = a(1)^2 + 7.

8 = a + 7.

Subtracting 7 from both sides, we get: 1 = a.

Finally, we substitute this value of "a" back into our equation: y = 1(x + 4)^2 + 7.

And there you have it! The equation of the parabola in vertex form is y = (x + 4)^2 + 7. This parabola sure knows how to make its mark on the coordinate plane.

To find the equation of the parabola in vertex form, we can use the vertex form equation of a parabola:

y = a(x-h)^2 + k

where (h, k) represents the vertex of the parabola. In this case, the given vertex is (-4, 7), so we have h = -4 and k = 7.

Now we need to find the value of "a" in the equation. To do this, we can substitute the coordinates (-3, 8) into the equation and solve for "a".

8 = a(-3 - (-4))^2 + 7
8 = a(-3 + 4)^2 + 7
8 = a(1)^2 + 7
8 = a + 7
a = 8 - 7
a = 1

Now that we have the value of "a", we can write the equation of the parabola in vertex form.

y = 1(x - (-4))^2 + 7
y = (x + 4)^2 + 7

Therefore, the equation of the parabola in vertex form is y = (x + 4)^2 + 7.

To write the equation of the parabola in vertex form, we can use the standard form of a parabola equation: y = a(x - h)^2 + k, where (h, k) is the vertex coordinates.

Given that the vertex is (-4, 7), we have h = -4 and k = 7. So, the equation so far is y = a(x + 4)^2 + 7.

To find the value of "a", we can use the point (-3, 8) which lies on the parabola. Substituting these coordinates into the equation, we have:

8 = a(-3 + 4)^2 + 7
8 = a(1)^2 + 7
8 = a + 7
a = 8 - 7
a = 1

Now, we can substitute the value of "a" into the equation, giving us the final equation of the parabola in vertex form:

y = 1(x + 4)^2 + 7

So, the equation of the parabola in vertex form is y = (x + 4)^2 + 7.