Question

I need a quadratic function that has an x intercept of(4,0)
And another function that has an x intercept of(-4,0)

Answer 1

so let x = 4 be a zero then x -4 is a factor

so you just need another factor...

then multiply them together to get the standard form or the quadratic

Answer 2

for the 2nd function

if x = -4 is an intercept or zero, then x + 4 is a factor

so same as above...

or you could combine both factors.

Answer 3

how do I get the other factor @campbell_st

Answer 4

well you can use the same value... the quadratic is a perfect square

so if you want another factor... let an x intercept by (-1, 0)

so what factor would you get from this point..?

Answer 5

(1,0)? @campbell_st

Answer 6

well a zero or intercept is at x = -1 so then x + 1 is a factor

you can use this for both questions

y = (x-4)(x+1)

part 2

y = (x +4)(x + 1)

Answer 7

oh I see

Answer 8

I got the answer wrong @campbell_st

Answer 9

it asks for a parabola that opens upward and one that opens downward

Answer 10

well you can have a perfect square

\[y = (x -4)^2\]

is there any other information in the question that you didn't include..?

Answer 11

the example of

\[y=(x -4)(x+1) = x^2 -3x - 4\]

will open upwards, because the coefficient of x^2 is positive.

Answer 12

yeah I put that and it says its wrong

Answer 13

Idk why because the x intercept is 4

Answer 14

Find two quadratic functions, one that opens upward and one that opens downward, whose graphs have the given x-intercepts. (There are many correct answers.)

(−4, 0), (4, 0)

Answer 15

ok... so the intercepts are

x = -4 so x + 4 is a factor

x = 4 so x - 4 is a factor

so the quadratic is

\[y = a(x -4)(x +4)\]

or

\[y = a(x^2 - 16)\]

for upwards make a a positive number and multiply, 1 is probably easiest

for downwards pick a negative number for a

so maybe a = -1 and then multiply out...

that should help you get the correct answer

Answer 16

ok let me plug it in

Answer 17

thank you