What is the axis of symmetry for the functionf(x)=7−4x+x2f(x)=7-4x+x^2f(x)=7−4x+x2?

Step 1: Define the Problem

Identify the axis of symmetry for the quadratic function $f(x) = 7 - 4x + x^2$.

Step 2: Break Down the Problem

The axis of symmetry for a quadratic function in the form $ax^2 + bx + c$ is given by the formula: $x = -\frac{b}{2a}$ Here, the function is $f(x) = x^2 - 4x + 7$, so $a = 1$, $b = -4$, and $c = 7$.

Step 3: Apply Relevant Concepts

Substitute the values of $a$ and $b$ into the formula for the axis of symmetry: $x = -\frac{-4}{2 \times 1}$

Step 4: Analysis, Verify and Summarize

Calculate the axis of symmetry: $x = \frac{4}{2} = 2$ Verify by checking the calculation:

• The formula $x = -\frac{b}{2a}$ is correctly applied.
• Substituting $b = -4$ and $a = 1$ gives $x = 2$.

Final Answer

The axis of symmetry for the function $f(x) = 7 - 4x + x^2$ is $x = 2$.