https://file.aiquickdraw.com/mathbot/file/1729129877461eggumsk9.jpg

Let's break down the first problem from the image:

The given function is:

\[
a(x) = (x - 5)(x + 6)
\]

### 1. **Finding the Zeros:**
To find the zeros, set each factor equal to zero:

- \(x - 5 = 0 \Rightarrow x = 5\)
- \(x + 6 = 0 \Rightarrow x = -6\)

So, the zeros are \(x = 5\) and \(x = -6\).

### 2. **Constant Term:**
The constant term is found by multiplying the constants from the factors:

\[
(-5) \times (6) = -30
\]

So, the constant term is \(-30\).

### 3. **Standard Form:**
Now, expand the binomials to convert to standard form:

\[
a(x) = (x - 5)(x + 6)
\]
Use the distributive property (FOIL method):

\[
a(x) = x^2 + 6x - 5x - 30
\]
\[
a(x) = x^2 + x - 30
\]

So, in standard form, the function is:

\[
a(x) = x^2 + x - 30
\]

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Let me know if you want more details or have any questions! Here are some follow-up questions:

1. Can you calculate the vertex of this parabola?
2. How would you graph this function using the zeros and vertex?
3. What is the axis of symmetry for the function \(a(x)\)?
4. What are the y-intercepts of the function \(a(x)\)?
5. Can you factor the standard form back into the factored form?

**Tip:** When converting to standard form, always remember to combine like terms after expanding the binomials.

Solve the quadratic equation a(x) = (x - 5)(x + 6). Find the zeros, constant term, and convert to standard form.

Learn how to solve the quadratic equation (x - 5)(x + 6). This problem involves finding the zeros, determining the constant term, and converting the equation to standard form. Suitable for Grades 8-10 students.

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