Question

find the y - intercept, the axis of symmetry, and the vertex of the graph of the function f(x) = -2x² + 4x - 7. the y - intercept is (0, -7) (type an ordered pair). the axis of symmetry is x = -2 (simplify your answer. type an equation).

Explanation:

Step1: Find the y - intercept

To find the y - intercept, we set \(x = 0\) in the function \(f(x)=-2x^{2}+4x - 7\).
Substitute \(x = 0\) into the function: \(f(0)=-2(0)^{2}+4(0)-7=-7\). So the y - intercept is \((0,-7)\).

Step2: Find the axis of symmetry

For a quadratic function in the form \(f(x)=ax^{2}+bx + c\) (\(a
eq0\)), the formula for the axis of symmetry is \(x =-\frac{b}{2a}\).
In the function \(f(x)=-2x^{2}+4x - 7\), we have \(a=-2\) and \(b = 4\).
Substitute \(a=-2\) and \(b = 4\) into the formula: \(x=-\frac{4}{2\times(-2)}=-\frac{4}{-4}=1\).

Step3: Find the vertex

The x - coordinate of the vertex is the same as the axis of symmetry, so \(x = 1\).
To find the y - coordinate of the vertex, we substitute \(x = 1\) into the function \(f(x)=-2x^{2}+4x - 7\).
\(f(1)=-2(1)^{2}+4(1)-7=-2 + 4-7=-5\). So the vertex is \((1,-5)\).

Answer:

• y - intercept: \((0,-7)\)
• Axis of symmetry: \(x = 1\)
• Vertex: \((1,-5)\) (Note: The original answer for the axis of symmetry was incorrect. The correct axis of symmetry for \(f(x)=-2x^{2}+4x - 7\) is \(x = 1\))