Question

find the y - intercept, the axis of symmetry, and the vertex of the graph of the function
$f(x) = -2x^2 + 4x - 7$

Explanation:

Step1: Find the y - intercept

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

Step2: Find the axis of symmetry

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

Step3: Find the vertex

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

Answer:

• y - intercept: \(-7\)
• Axis of symmetry: \(x = 1\)
• Vertex: \((1,-5)\)