Write a quadratic function f shoes zeros are -3 and 10

Answer 1

Short answer: y = x² - 7x - 10

Long Answer:

Use your roots and set them up as binomials.

Polynomials have a property where they will equate to zero when the variable of interest is equal to the root.

First order binomials (exponent of 1) can be expressed as:

(x - a)

where a = root

To find a root of a polynomial, set it equal to zero:

x - a = 0

x = a

A quadratic equation is the product of two first order binomials:

y = (x-a)(x-b)

So let’s test this property defined above:

Set y = 0,

0 = (x-a)(x-b)

if we divide by (x-b):

0 = (x-a)

x = a

this is our first root

if we divide by (x-a):

0 = (x-b)

x = b

this is our second root

back to the point, we can plug in our two roots:

y = (x-(-3))(x-10)

y = (x+3)(x-10)

we find the product through FOIL:

(x•x) + (-10 • x) + (3 • x) + (3 • -10)

y = x^2 - 10x + 3x - 10

y = x^2 - 7x - 10

Answer 2