Answer:
- A(-9/2, 0)
- B(1, 0)
- C(0, -9)
Explanation:
Given the quadratic equation y = 2x² +7x -9, you want the coordinates of the x- and y-intercepts.
X-intercepts
The values of x where y=0 can be found by factoring the equation.
y = (2x +9)(2x -2)/2 = (2x +9)(x -1)
The constants 9 and -2 in the binomial terms are factors of the product of leading and trailing coefficients (2)(-9) = -18. Those factors are chosen because their sum is 7, the middle coefficient.
The x-intercepts are the values of x that make these factors zero:
2x +9 = 0 ⇒ x = -9/2
x -1 = 0 ⇒ x = 1
Points A and B are ...
Y-intercept
The y-value at point C is where x=0. It is the constant in the quadratic equation.
y = 2(0²) +7(0) -9 = -9
Point C is ...