Solved on Mar 02, 2024

Write a quadratic function $f(m) = m^2 + bm + c$ with roots at 18 and $P$ .

STEP 1

Assumptions
1. The leading coefficient of the quadratic function is 1.
2. The roots of the quadratic function are 18 and $P$ .
3. The quadratic function is in the form $f(m) = am^2 + bm + c$ , where $a = 1$ .

STEP 2

The roots of a quadratic function $f(m) = m^2 + bm + c$ can be used to write the function in its factored form as follows:
$f(m) = (m - root_1)(m - root_2)$

STEP 3

Substitute the given roots into the factored form of the quadratic function.
$f(m) = (m - 18)(m - P)$

STEP 4

Expand the factored form to get the quadratic function in standard form.
$f(m) = m^2 - Pm - 18m + 18P$

STEP 5

Combine like terms to simplify the expression.
$f(m) = m^2 - (P + 18)m + 18P$

STEP 6

The quadratic function with the leading coefficient 1 and roots 18 and $P$ is:
$f(m) = m^2 - (P + 18)m + 18P$

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Write a quadratic function $f(m) = m^2 + bm + c$ with roots at 18 and $P$ .

STEP 1

Assumptions
1. The leading coefficient of the quadratic function is 1.
2. The roots of the quadratic function are 18 and $P$ .
3. The quadratic function is in the form $f(m) = am^2 + bm + c$ , where $a = 1$ .

STEP 2

The roots of a quadratic function $f(m) = m^2 + bm + c$ can be used to write the function in its factored form as follows:
$f(m) = (m - root_1)(m - root_2)$

STEP 3

Substitute the given roots into the factored form of the quadratic function.
$f(m) = (m - 18)(m - P)$

STEP 4

Expand the factored form to get the quadratic function in standard form.
$f(m) = m^2 - Pm - 18m + 18P$

STEP 5

Combine like terms to simplify the expression.
$f(m) = m^2 - (P + 18)m + 18P$

STEP 6

The quadratic function with the leading coefficient 1 and roots 18 and $P$ is:
$f(m) = m^2 - (P + 18)m + 18P$

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Write a quadratic function f(m)=m2+bm+cf(m) = m^2 + bm + cf(m)=m2+bm+c with roots at 18 and PPP.

STEP 1

Assumptions1. The leading coefficient of the quadratic function is 1.2. The roots of the quadratic function are 18 and P P P.3. The quadratic function is in the form f(m)=am2+bm+c f(m) = am^2 + bm + c f(m)=am2+bm+c, where a=1 a = 1 a=1.

STEP 2

The roots of a quadratic function f(m)=m2+bm+c f(m) = m^2 + bm + c f(m)=m2+bm+c can be used to write the function in its factored form as follows:f(m)=(m−root1)(m−root2) f(m) = (m - root_1)(m - root_2) f(m)=(m−root1​)(m−root2​)

STEP 3

Substitute the given roots into the factored form of the quadratic function.f(m)=(m−18)(m−P) f(m) = (m - 18)(m - P) f(m)=(m−18)(m−P)

STEP 4

Expand the factored form to get the quadratic function in standard form.f(m)=m2−Pm−18m+18P f(m) = m^2 - Pm - 18m + 18P f(m)=m2−Pm−18m+18P

STEP 5

Combine like terms to simplify the expression.f(m)=m2−(P+18)m+18P f(m) = m^2 - (P + 18)m + 18P f(m)=m2−(P+18)m+18P

STEP 6

The quadratic function with the leading coefficient 1 and roots 18 and P P P is:f(m)=m2−(P+18)m+18P f(m) = m^2 - (P + 18)m + 18P f(m)=m2−(P+18)m+18P

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Write a quadratic function $f(m) = m^2 + bm + c$ with roots at 18 and $P$ .

Assumptions
1. The leading coefficient of the quadratic function is 1.
2. The roots of the quadratic function are 18 and $P$ .
3. The quadratic function is in the form $f(m) = am^2 + bm + c$ , where $a = 1$ .

The roots of a quadratic function $f(m) = m^2 + bm + c$ can be used to write the function in its factored form as follows:
$f(m) = (m - root_1)(m - root_2)$

Substitute the given roots into the factored form of the quadratic function.
$f(m) = (m - 18)(m - P)$

Expand the factored form to get the quadratic function in standard form.
$f(m) = m^2 - Pm - 18m + 18P$

Combine like terms to simplify the expression.
$f(m) = m^2 - (P + 18)m + 18P$

The quadratic function with the leading coefficient 1 and roots 18 and $P$ is:
$f(m) = m^2 - (P + 18)m + 18P$