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.) (-3/2,0) , (1, 0)

Question

opens upward, y=

opens upward, y=

Answer 1

Hi Aerin H

With (-3/2,0) and (1,0)

In order for x to be -3/2 we could have 2x = -3, as a set up to avoid fractions in the quadratic.

For x to be equal to 1, (x - 1) = 0

(2x + 3)(x - 1)

Positive Quadratic opens upward

f(x) = 2x² + x - 3

Negative Quadratic opens downward

(3 + 2x)(1 - x)

f(x) = -2x² - x + 3

Answer 2

x = -3/2 and x=1

Equation which opens up:

(x+3/2)(x-1)=0

x² -1x + 3/2x -3/2

Y = x² +1/2x -3/2

Equation which opens down:

-1(x+3/2)(x-1)=0

-1(x² -1x + 3/2x -3/2)

Y = -x² - 1/2x + 3/2