Write the equation of the parabola in standard form:
𝑥2−4𝑦+3=7

We are given the equation:

\[
x^2 - 4y + 3 = 7
\]

### Step 1: Simplify the equation
Subtract 3 from both sides to isolate the terms involving \(y\):

\[
x^2 - 4y = 7 - 3
\]
\[
x^2 - 4y = 4
\]

### Step 2: Solve for \(y\)
Now, isolate \(y\) on one side of the equation:

\[
-4y = -x^2 + 4
\]

Divide both sides by \(-4\):

\[
y = \frac{x^2}{4} - 1
\]

### Step 3: Write the equation in standard form
The equation of the parabola in standard form is:

\[
y = \frac{1}{4}x^2 - 1
\]

This is the equation of a parabola that opens upwards, with its vertex at \((0, -1)\).

Would you like more details on solving this type of equation?

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Here are 5 related questions to deepen your understanding:

1. How can you determine the direction a parabola opens based on its equation?
2. What is the vertex form of a parabola, and how does it relate to the standard form?
3. How do you find the focus and directrix of a parabola from its equation?
4. Can you rewrite the given equation as a perfect square form?
5. How does changing the coefficient of \(x^2\) affect the shape of the parabola?

**Tip:** The sign of the coefficient in front of \(x^2\) or \(y^2\) helps determine whether the parabola opens up, down, left, or right.

Write the equation of the parabola in standard form: x^2 - 4y + 3 = 7

Learn how to convert the equation of a parabola x^2 - 4y + 3 = 7 into standard form. This solution walks through the simplification steps and explains key algebraic concepts, such as isolating y and identifying the vertex of the parabola. Perfect for students in Grades 9-10.

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