Asked by Alisa Jackson on Sep 23, 2024
Verified
Find the intercepts of y=9x2−8x+8y = 9 x ^ { 2 } - 8 x + 8y=9x2−8x+8 .
A) x -intercept: (−49,0) \left( - \frac { 4 } { 9 } , 0 \right) (−94,0) y -intercepts: (0,8)
B) no x -intercepts y -intercept: (0,8)
C) x -intercept: (8,0) no y -intercepts
D) no x -intercepts y -intercept: (0,-8)
E) x -intercept: (8,0) y -intercept: (0,8)
Intercepts
Points where a graph intersects the axes; the x-intercept is where the graph crosses the x-axis, and the y-intercept is where it crosses the y-axis.
Parabola
A specific type of curve on a graph, represented by a quadratic function, characterized by its symmetric shape which can open upwards or downwards.
- Determine the intercepts of quadratic functions.
Verified Answer
OP
omolayo popoolaabout 7 hours ago
Final Answer :
B
Explanation :
To find the y-intercept, set x=0x = 0x=0 , which gives y=8y = 8y=8 , so the y-intercept is (0,8). For the x-intercepts, solve 9x2−8x+8=09x^2 - 8x + 8 = 09x2−8x+8=0 . The discriminant of this quadratic equation is b2−4ac=(−8)2−4(9)(8)=64−288=−224b^2 - 4ac = (-8)^2 - 4(9)(8) = 64 - 288 = -224b2−4ac=(−8)2−4(9)(8)=64−288=−224 , which is negative, indicating there are no real x-intercepts.
Learning Objectives
- Determine the intercepts of quadratic functions.