Questions: QUESTION 5 Find the zeros of the following parabola: f(x)=x^2-6x+8 (2,0),(4,0) (0,4),(0,2) (0,-2),(0,-4) (-2,0),(-4,0)

Transcript text: QUESTION 5 Find the zeros of the following parabola: $f(x)=x^{2}-6 x+8$ $\{(2,0),(4,0)\}$ $\{(0,4),(0,2)\}$ $\{(0,-2),(0,-4)\}$ $\{(-2,0),(-4,0)\}$

Solution

Solution Steps

To find the zeros of the parabola $ f(x) = x^2 - 6x + 8 $, we need to solve the equation $ x^2 - 6x + 8 = 0 $. This can be done by factoring the quadratic equation.

Step 1: Set the Quadratic Equation to Zero

To find the zeros of the quadratic function $ f(x) = x^2 - 6x + 8 $, we need to solve the equation: \[ x^2 - 6x + 8 = 0 \]

Step 2: Factor the Quadratic Equation

We factor the quadratic equation: \[ x^2 - 6x + 8 = (x - 2)(x - 4) \]

Step 3: Solve for the Zeros

Set each factor equal to zero and solve for $ x $: \[ x - 2 = 0 \quad \Rightarrow \quad x = 2 \] \[ x - 4 = 0 \quad \Rightarrow \quad x = 4 \]