https://file.aiquickdraw.com/mathbot/file/1727643563960s3pm8b3n.jpg

The graph shows a quadratic function, and we are tasked with finding its equation in standard form.

### Step 1: General form of a quadratic function
The standard form of a quadratic function is:
\[
y = ax^2 + bx + c
\]
We can also use the **vertex form** of a quadratic function to find the equation, which is:
\[
y = a(x - h)^2 + k
\]
where \((h, k)\) is the vertex.

### Step 2: Identify the vertex
From the graph, the vertex is clearly \((2, -6)\). So, \(h = 2\) and \(k = -6\).

Thus, the equation becomes:
\[
y = a(x - 2)^2 - 6
\]

### Step 3: Use another point to find "a"
Now, we need to find the value of \(a\). We can use another point on the graph to do this. The point \((5, 3)\) lies on the parabola. Plug this point \((x, y) = (5, 3)\) into the vertex form of the equation:

\[
3 = a(5 - 2)^2 - 6
\]
\[
3 = a(3)^2 - 6
\]
\[
3 = 9a - 6
\]
\[
9 = 9a
\]
\[
a = 1
\]

### Step 4: Write the equation in vertex form
Now that we know \(a = 1\), the equation in vertex form is:
\[
y = (x - 2)^2 - 6
\]

### Step 5: Convert to standard form
Finally, let's expand this equation into standard form:
\[
y = (x - 2)^2 - 6
\]
\[
y = (x^2 - 4x + 4) - 6
\]
\[
y = x^2 - 4x - 2
\]

Thus, the equation of the quadratic function in standard form is:
\[
y = x^2 - 4x - 2
\]

Would you like more details on any part of this process or have any questions?

### Related Questions:
1. How do you find the vertex of a parabola from its equation in standard form?
2. What are the differences between vertex form and standard form of a quadratic equation?
3. How can you determine the direction of a parabola from its equation?
4. How do you find the x-intercepts of a quadratic equation?
5. How does changing the value of "a" affect the shape of a parabola?

### Tip:
When working with quadratic functions, always check the vertex and another point on the graph to accurately determine the function's parameters.

The graph represents a quadratic function. Write an equation of the function in standard form.

Learn how to find the quadratic equation of a parabola with vertex (2, -6) and point (5, 3). This tutorial covers both vertex form and converting to standard form for Grades 9-10 students.

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