Answer:
a) y-int is at (0, 8)
b) zeros are at (0.8, 0) and (-3.2, 0); after having rounded to the nearest tenth.
Step-by-step explanation:
Given that y = -3x² - 7x + 8
we can find our y-intercept by setting x = 0
y = -3 (0)² - 7 (0) + 8
y = 8
so, our y intercept is at (8, 0)
To find our zeros, or x-intercepts, we need to set y = 0
0 = -3x² - 7x + 8
Let's use the quadratic formula
x = (-b ± √(b² - 4 (a * c))) / 2a
where, in this case
a = -3
b = -7
c = 8
x = (7 ± √((-7)² - 4 (-3 * 8))) / (2 * -3)
x = (7 ± √(49 - -96) / -6
x = (7 ± √145) / -6
using the addition pathway
x = (7 + √145) / -6
x = 3.2
using the subtraction pathway
x = (7 - √145) / -6
x = -0.8
So, our x-intercepts, or zeros, will lie on the points
(0.8, 0) and (-3.2, 0)
Create a table of x and y values using the given equation, and plot and graph. Clearly label your y and x intercepts.
(x, y)
(-3, 2)
(-2, 10)
(-1, 12)
(0, 8)
(1, -2)
(2, -18)
(3, -40)
