https://file.aiquickdraw.com/mathbot/file/1729704407975whblvgdk.jpg

The equation given in the image is \( f(x) = -x^2 + 4x + 3 \), which is a quadratic function. To identify the vertex and the y-intercept, let's break it down.

### 1. **Finding the Vertex**:
The equation is in standard form \( f(x) = ax^2 + bx + c \). For a quadratic function \( ax^2 + bx + c \), the vertex \( x \)-coordinate is given by:
\[
x = \frac{-b}{2a}
\]
In your equation, \( a = -1 \), \( b = 4 \), and \( c = 3 \). So:
\[
x = \frac{-4}{2(-1)} = 2
\]
Now, substitute \( x = 2 \) back into the equation to find the \( y \)-coordinate of the vertex:
\[
f(2) = -(2)^2 + 4(2) + 3 = -4 + 8 + 3 = 7
\]
Thus, the vertex is \( (2, 7) \).

### 2. **Finding the Y-Intercept**:
The y-intercept occurs when \( x = 0 \). Substituting \( x = 0 \) into the equation:
\[
f(0) = -(0)^2 + 4(0) + 3 = 3
\]
Thus, the y-intercept is \( (0, 3) \).

### Summary:
- **Vertex**: \( (2, 7) \)
- **Y-Intercept**: \( (0, 3) \)

Would you like details on how to graph it, or do you have further questions?

### Related Questions:
1. How do you graph quadratic functions step by step?
2. What is the importance of the axis of symmetry in a parabola?
3. How do you calculate the roots of a quadratic equation using factoring or the quadratic formula?
4. What is the significance of the sign of \( a \) (whether the parabola opens upwards or downwards)?
5. How does the vertex form of a quadratic function compare to the standard form?

### Tip:
The vertex form of a quadratic function is useful for quickly identifying the vertex without needing calculations. You can rewrite the standard form to the vertex form by completing the square!

Identify the vertex and the y-intercept then graph f(x) = -x^2 + 4x + 3.

Learn how to find the vertex and y-intercept of the quadratic function f(x) = -x^2 + 4x + 3, using the vertex formula and graphing techniques. Suitable for students in Grades 9-10, this problem covers core algebraic concepts.

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