Questions: Identify the vertex of the graph of the quadratic function. f(x)=x^2-1

Transcript text: Identify the vertex of the graph of the quadratic function. \[ f(x)=x^{2}-1 \]

Solution

Solution Steps

Step 1: Identify the Coefficients

The quadratic function is given by \( f(x) = x^2 - 1 \). This can be expressed in the standard form \( ax^2 + bx + c \), where:

\( a = 1 \)
\( b = 0 \)
\( c = -1 \)

Step 2: Calculate the x-coordinate of the Vertex

The x-coordinate of the vertex of a quadratic function can be found using the formula: \[ x = -\frac{b}{2a} \] Substituting the values of \( a \) and \( b \): \[ x = -\frac{0}{2 \times 1} = 0 \]

Step 3: Calculate the y-coordinate of the Vertex

Substitute \( x = 0 \) back into the function to find the y-coordinate: \[ f(0) = (0)^2 - 1 = -1 \]

Final Answer

The vertex of the graph of the quadratic function \( f(x) = x^2 - 1 \) is \((0, -1)\).

\[ \boxed{(0, -1)} \]

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