Find the formula, in standard form  
y
=
a
x
2
+
b
x
+
c
 , for a quadratic that has roots at x = -7 and x = 6, and has leading coefficient of 1.

y =

The quadratic equation with roots \(x = -7\) and \(x = 6\) can be written using the factored form of a quadratic equation:

\[
y = a(x - r_1)(x - r_2)
\]

where \(r_1\) and \(r_2\) are the roots, and \(a\) is the leading coefficient.

Given the roots \(r_1 = -7\) and \(r_2 = 6\), and the leading coefficient \(a = 1\), we can substitute these values into the factored form:

\[
y = 1(x + 7)(x - 6)
\]

Now, expand the equation:

\[
y = (x + 7)(x - 6)
\]

Use the distributive property (also known as FOIL) to expand:

\[
y = x^2 - 6x + 7x - 42
\]

Simplify the terms:

\[
y = x^2 + x - 42
\]

Thus, the quadratic equation in standard form is:

\[
y = x^2 + x - 42
\]

Would you like more details or have any questions?

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Here are five related questions you might find interesting:
1. How do you determine the axis of symmetry for this quadratic equation?
2. What is the vertex of the quadratic \(y = x^2 + x - 42\)?
3. How do you find the y-intercept of this quadratic equation?
4. What does the discriminant of this quadratic equation tell us about its roots?
5. Can we rewrite this equation in vertex form?

**Tip:** The sum of the roots of a quadratic equation is always \(-\frac{b}{a}\), and the product of the roots is \(\frac{c}{a}\).

Find the formula, in standard form y = ax^2 + bx + c, for a quadratic that has roots at x = -7 and x = 6, and has a leading coefficient of 1.

Learn how to find the quadratic equation with roots at x = -7 and x = 6, with a leading coefficient of 1. This problem involves key algebraic concepts such as factoring and expanding using the distributive property (FOIL). Suitable for students in Grades 9-10.

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Find the formula, in standard form
y

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