Features of Graphs of Quadratic Equations Practice

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

To determine the vertex and axis of symmetry of the quadratic equation \( y = x^2 - 10x + 3 \), we can use the vertex formula, which is given by:

• The x-coordinate of the vertex \( x = -\frac{b}{2a} \)
• The corresponding y-coordinate can be found by substituting this x-value back into the equation.

From the equation \( y = x^2 - 10x + 3 \), we identify:

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

Now, we calculate the x-coordinate of the vertex:

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

Next, we find the y-coordinate by substituting \( x = 5 \) back into the equation:

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

So, the vertex is \( (5, -22) \).

The axis of symmetry, which is a vertical line that passes through the vertex, is given by the equation:

\[ x = 5 \]

Putting this all together, we have:

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

So your final answer is:

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