To find the vertex and write the equation in standard form (parabola equation) from the points \((-4,1)\) and \((-3,4)\), we'll assume these points lie on a parabola. 

However, you need at least three points to uniquely define a parabola. Since only two points are given, I'll demonstrate the process to find the equation of a parabola in standard form by introducing the vertex formula. Let's assume that one of these points is the vertex.

The equation of a parabola in standard form is:

\[
y = ax^2 + bx + c
\]

If we assume that the vertex is \((-3,4)\), we can use the vertex form of the parabola equation:

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

Where \((h, k)\) is the vertex. Here, the vertex is \((-3,4)\), so:

\[
y = a(x + 3)^2 + 4
\]

Now, we'll use the point \((-4,1)\) to solve for \(a\):

1. Plug \((-4, 1)\) into the equation:

\[
1 = a(-4 + 3)^2 + 4
\]

2. Simplify:

\[
1 = a(1)^2 + 4
\]
\[
1 = a + 4
\]

3. Solve for \(a\):

\[
a = 1 - 4 = -3
\]

Now we have the equation:

\[
y = -3(x + 3)^2 + 4
\]

This is the vertex form of the equation. To convert this into standard form, expand the equation:

\[
y = -3(x^2 + 6x + 9) + 4
\]
\[
y = -3x^2 - 18x - 27 + 4
\]
\[
y = -3x^2 - 18x - 23
\]

Thus, the equation of the parabola in standard form is:

\[
y = -3x^2 - 18x - 23
\]

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### Related Questions:
1. How do you convert from vertex form to standard form in general?
2. What is the significance of the vertex in a parabola's equation?
3. How can you find the vertex if it's not directly given?
4. How do you find the axis of symmetry from a quadratic equation?
5. How do you calculate the focus and directrix of a parabola?

### Tip:
Always ensure that you have enough points (at least three) to define a parabola uniquely. Two points only help in specific cases, such as if one of them is the vertex.

Find the vertex and the standard form of the parabola given points (-4,1) and (-3,4).

This problem demonstrates how to find the vertex and convert the vertex form of a parabola to the standard form using points (-4, 1) and (-3, 4). Learn key algebraic concepts and formulas, suitable for students in Grades 9-11.

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