Identify the information for the quadratic function below.Must show work/steps on your work page𝑦=𝑥2 −4⁢𝑥+13Find the axis of symmetry:  x = Find the vertex: (, )Find the y-intercept

Sure, let's go through the steps to find the axis of symmetry, the vertex, and the y-intercept for the quadratic function $y = x^2 - 4x + 13$.

Step 1: Find the Axis of Symmetry

The axis of symmetry for a quadratic function in the form $y = ax^2 + bx + c$ can be found using the formula: $x = -\frac{b}{2a}$

For the given function $y = x^2 - 4x + 13$:

• $a = 1$
• $b = -4$
• $c = 13$

Plug these values into the formula: $x = -\frac{-4}{2 \cdot 1}$ $x = \frac{4}{2}$ $x = 2$

So, the axis of symmetry is $x = 2$.

Step 2: Find the Vertex

The vertex of a quadratic function is located at the point $(h, k)$, where $h$ is the x-coordinate of the axis of symmetry, and $k$ is the value of the function at $x = h$.

We already found $h = 2$. Now, we need to find $k$ by substituting $x = 2$ into the original function: $y = (2)^2 - 4(2) + 13$ $y = 4 - 8 + 13$ $y = 9$

So, the vertex is $(2, 9)$.

Step 3: Find the Y-Intercept

The y-intercept of a function is the point where the graph intersects the y-axis. This occurs when $x = 0$.

Substitute $x = 0$ into the original function: $y = (0)^2 - 4(0) + 13$ $y = 0 - 0 + 13$ $y = 13$

So, the y-intercept is $(0, 13)$.

Summary

• Axis of symmetry: $x = 2$
• Vertex: $(2, 9)$
• Y-intercept: $(0, 13)$