Finding Quadratic Function from Intercepts: Step-by-Step Guide

TLDR; Finding a quadratic function given the intercepts, factoring, and determining the value of 'A'.

💡 Finding the Quadratic Function

Given the intercepts of the quadratic function, the goal is to find the quadratic function in factored form.

The factored form of a quadratic function with intercepts R sub 1 and R sub 2 can be given by F of X = 'A' times the factor of X - R sub 1 times the factor of X - R sub 2.

By substituting the given intercepts into the factored form, the function can be determined as F of X = 'A' times the quantity X + 4 times the quantity X - 3.

🔍 Using Y Intercept to Find 'A'

The point (0, 6) on the graph is used to determine the value of 'A'.

Substituting 0 for X, the function value must be 6, and using this information, the value of 'A' can be solved for.

The calculation leads to the determination of 'A' as -1/2, resulting in the function in factored form as F of X = -1/2 times the quantity X + 4 times the quantity X - 3.

📈 Final Result

The quadratic function graphed with the given intercepts is represented by F of X = -1/2 times the quantity X + 4 times the quantity X - 3.

The video concludes with the mention of the potential need to express the function in general form by multiplying it out.