Question

Determine the vertex and axis of symmetry of y=x2−10x+3
𝑦
=
𝑥
2
−
10
𝑥
+
3
.(1 point)
vertex: (); axis of symmetry: x=
𝑥
=

Answer 1

To find the vertex and axis of symmetry of the quadratic function \( y = x^2 - 10x + 3 \), we can use the vertex form of a parabola or the vertex formula.

The standard form of a quadratic function is \( y = ax^2 + bx + c \). For the given quadratic:

- \( a = 1 \)
- \( b = -10 \)
- \( c = 3 \)

### Step 1: Finding the x-coordinate of the vertex

The x-coordinate of the vertex can be found using the formula:

\[
x = -\frac{b}{2a}
\]

Substituting the values of \( a \) and \( b \):

\[
x = -\frac{-10}{2 \cdot 1} = \frac{10}{2} = 5
\]

### Step 2: Finding the y-coordinate of the vertex

To find the y-coordinate of the vertex, substitute \( x = 5 \) back into the original equation:

\[
y = (5)^2 - 10(5) + 3
\]
\[
y = 25 - 50 + 3
\]
\[
y = -22
\]

### Conclusion

The vertex of the parabola is at the point \( (5, -22) \).

### Step 3: Finding the axis of symmetry

The axis of symmetry for a quadratic function in standard form is given by the equation \( x = \) (the x-coordinate of the vertex). Thus, the axis of symmetry is:

\[
x = 5
\]

### Final Answer

Vertex: \( (5, -22) \); Axis of symmetry: \( x = 5 \)