Find the x-coordinate of vertex of the following quadratic function. 𝑓(𝑥)=−1𝑥2+4𝑥+5

1. Break Down the Problem

To find the x-coordinate of the vertex of the quadratic function $f(x) = -1x^2 + 4x + 5$, we can use the formula for the x-coordinate of the vertex of a parabola given by: $x = -\frac{b}{2a}$ where $a$ and $b$ are the coefficients from the quadratic equation in the standard form $ax^2 + bx + c$.

2. Relevant Concepts

In the given function, we identify:

• $a = -1$
• $b = 4$
• $c = 5$

3. Analysis and Detail

Now, substituting the values of $a$ and $b$ into the vertex formula: $x = -\frac{4}{2 \times -1}$

4. Verify and Summarize

Calculating this gives: $x = -\frac{4}{-2} = 2$

Final Answer

The x-coordinate of the vertex of the quadratic function $f(x) = -1x^2 + 4x + 5$ is $x = 2$.