write the standard form. identify a,b,and c y=-(x+5)^2+9

To write the equation \( y = -(x+5)^2 + 9 \) in **standard form**, we first expand the equation.

### Step 1: Expand \( (x+5)^2 \)
\[
(x+5)^2 = x^2 + 10x + 25
\]

### Step 2: Substitute into the equation
\[
y = -(x^2 + 10x + 25) + 9
\]

### Step 3: Distribute the negative sign
\[
y = -x^2 - 10x - 25 + 9
\]

### Step 4: Combine like terms
\[
y = -x^2 - 10x - 16
\]

Thus, the **standard form** of the equation is:
\[
y = -x^2 - 10x - 16
\]

### Identifying the coefficients \(a\), \(b\), and \(c\):
- \(a = -1\)
- \(b = -10\)
- \(c = -16\)

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

Here are 5 related questions:
1. How do you graph a quadratic equation in standard form?
2. What does the value of \(a\) tell us about the graph's direction?
3. How do you find the vertex of a quadratic equation?
4. What is the difference between standard and vertex form of a quadratic equation?
5. How do you find the axis of symmetry for this equation?

**Tip:** The value of \(a\) in a quadratic equation determines whether the parabola opens upward (\(a > 0\)) or downward (\(a < 0\)).

write the standard form. identify a, b, and c y=-(x+5)^2+9

Learn how to convert the quadratic equation y=-(x+5)^2+9 to its standard form and identify the coefficients a, b, and c. This guide includes step-by-step instructions for expanding and simplifying the equation, suitable for students in Grades 9-10.

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