QuestionFind the value of $x$ that minimizes the function $f(x)=(x+7)^{2}+4$ .

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=(x+7)^{}+4$ . The function is a quadratic function, which is a parabola3. The parabola opens upwards because the coefficient of x^ is positive4. The minimum value of the function is the vertex of the parabola

STEP 2

The standard form of a quadratic function is $f(x) = a(x-h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.

STEP 3

Comparing the given function $f(x)=(x+7)^{2}+$ with the standard form, we can see that $h=-7$ and $k=$ .

STEP 4

Since the parabola opens upwards, the vertex of the parabola gives the minimum value of the function.

STEP 5

Therefore, the value of $x$ for which $f(x)$ reaches its minimum is $x=h=-7$ .
The value of $x$ for which $f(x)$ reaches its minimum is $x=-7$ .

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QuestionFind the value of $x$ that minimizes the function $f(x)=(x+7)^{2}+4$ .

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=(x+7)^{}+4$ . The function is a quadratic function, which is a parabola3. The parabola opens upwards because the coefficient of x^ is positive4. The minimum value of the function is the vertex of the parabola

STEP 2

The standard form of a quadratic function is $f(x) = a(x-h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.

STEP 3

Comparing the given function $f(x)=(x+7)^{2}+$ with the standard form, we can see that $h=-7$ and $k=$ .

STEP 4

Since the parabola opens upwards, the vertex of the parabola gives the minimum value of the function.

STEP 5

Therefore, the value of $x$ for which $f(x)$ reaches its minimum is $x=h=-7$ .
The value of $x$ for which $f(x)$ reaches its minimum is $x=-7$ .

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QuestionFind the value of xxx that minimizes the function f(x)=(x+7)2+4f(x)=(x+7)^{2}+4f(x)=(x+7)2+4.

Studdy Solution

STEP 1

Assumptions1. The function is f(x)=(x+7)+4f(x)=(x+7)^{}+4f(x)=(x+7)+4 . The function is a quadratic function, which is a parabola3. The parabola opens upwards because the coefficient of x^ is positive4. The minimum value of the function is the vertex of the parabola

STEP 2

The standard form of a quadratic function is f(x)=a(x−h)2+kf(x) = a(x-h)^2 + kf(x)=a(x−h)2+k, where (h,k)(h, k)(h,k) is the vertex of the parabola.

STEP 3

Comparing the given function f(x)=(x+7)2+f(x)=(x+7)^{2}+f(x)=(x+7)2+ with the standard form, we can see that h=−7h=-7h=−7 and k=k=k=.

STEP 4

Since the parabola opens upwards, the vertex of the parabola gives the minimum value of the function.

STEP 5

Therefore, the value of xxx for which f(x)f(x)f(x) reaches its minimum is x=h=−7x=h=-7x=h=−7.The value of xxx for which f(x)f(x)f(x) reaches its minimum is x=−7x=-7x=−7.

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QuestionFind the value of $x$ that minimizes the function $f(x)=(x+7)^{2}+4$ .

Assumptions1. The function is $f(x)=(x+7)^{}+4$ . The function is a quadratic function, which is a parabola3. The parabola opens upwards because the coefficient of x^ is positive4. The minimum value of the function is the vertex of the parabola

The standard form of a quadratic function is $f(x) = a(x-h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.

Comparing the given function $f(x)=(x+7)^{2}+$ with the standard form, we can see that $h=-7$ and $k=$ .

Therefore, the value of $x$ for which $f(x)$ reaches its minimum is $x=h=-7$ .
The value of $x$ for which $f(x)$ reaches its minimum is $x=-7$ .