Question

1. f(x)= (x+4)(x-6) 2. f(x)= (2x-4)(x-3)

Answer 1

The intercepts and the standard form of each polynomial are listed below:

1. x-Intercept: x = - 4 or x = 6, Standard form: f(x) = x² - 2 · x - 24, y-Intercept: f(0) = - 24
2. x-Intercept: x = 1 / 4 or x = 3, Standard form: f(x) = 2 · x² - 10 · x + 12, y-Intercept: f(0) = 12

How to find the intercepts and the standard form of quadratic equations

In this case we need to find the intercepts of each quadratic equation and transform each quadratic equation into standard form. The x-intercept correspond with each of the roots of the polynomial and the y-intercept is found by evaluating the expression at x = 0.

Now we proceed to find each element:

Case 1

x-Intercept

x = - 4 or x = 6

Standard form

f(x) = (x + 4) · (x - 6)

f(x) = x² - 2 · x - 24

y-Intercept

f(0) = - 24

Case 2

x-Intercept

x = 1 / 4 or x = 3

Standard form

f(x) = (2 · x - 4) · (x - 3)

f(x) = 2 · (x - 2) · (x - 3)

f(x) = 2 · (x² - 5 · x + 6)

f(x) = 2 · x² - 10 · x + 12

y-Intercept

f(0) = 12

To learn more on quadratic equations: brainly.com/question/1863222

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