Questions: Write a quadratic function f whose only zero is -7. f(x)=

Transcript text: Write a quadratic function $f$ whose only zero is -7 . \[ f(x)= \]

Solution

Step 1: Identify the zeros of the quadratic function

The given zeros are -7 and -7.

Step 2: Determine the general form of the quadratic function

Since the zeros are repeated, we use the form $f(x) = a(x - r)^2$ where $r = -7$.

Step 3: Incorporate the scaling factor

The scaling factor $a$ is 1, which determines the direction and stretch of the parabola.

Step 4: Write the quadratic function

The quadratic function is f(x) = 1(x - (-7))^2.

Step 5: Expand and simplify the quadratic function

After expanding and simplifying, the quadratic function is x^2 + 14x + 49.

The quadratic function given the zeros -7 and -7 with scaling factor 1 is x^2 + 14x + 49.

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