Problemas
Graph the function Identify the axis of symmetry and the vertex. f(x)=x^2-4x+7 The axis of symmetry is square (Type an equation.)
Roztwór
Daniela
professionell · Tutor durante 6 años
4.2
(268 Votos)
Respuesta
The axis of symmetry is
. The vertex is \((2, 3)\).
Explicación
## Step 1The given function is a quadratic function in the form \(f(x) = ax^2 + bx + c\), where
,
, and
.## Step 2The axis of symmetry for a quadratic function is given by the formula
.### **The formula for the axis of symmetry is
**## Step 3Substitute the values of
and
into the formula to find the axis of symmetry.## Step 4The vertex of the parabola is the point on the axis of symmetry that is also on the graph of the function. It is given by the point \((-\frac{b}{2a}, f(-\frac{b}{2a}))\).### **The formula for the vertex is \((-\frac{b}{2a}, f(-\frac{b}{2a}))\)**## Step 5Substitute the values of
,
, and
into the formula to find the vertex.