In the diagram, the curve y=9x2−9 cuts the x-axis at two points M and N. Find the coordinates of M and N.
Question
In the diagram, the curve cuts the x-axis at two points M and N.
Find the coordinates of M and N.
Solution
To find the points where the curve y = 9x^2 - 9 cuts the x-axis, we need to set y = 0 and solve for x. This is because the x-axis is defined by y = 0.
So, we have:
0 = 9x^2 - 9
We can simplify this equation by dividing through by 9:
0 = x^2 - 1
This is a difference of squares, which can be factored as follows:
0 = (x - 1)(x + 1)
Setting each factor equal to zero gives the solutions x = 1 and x = -1.
Therefore, the curve y = 9x^2 - 9 cuts the x-axis at the points M(1, 0) and N(-1, 0).
Similar Questions
Which of the following points represents the x-intercepts of the quadratic equation y = x2 + 9x?
Select the equation of the line that is perpendicular to y = 9 and passes through the point (5, 2).
Which of the following represents the x-intercepts and the vertex of the quadratic relation y = −x2 − 6x + 27?
A line has a y-intercept of 5 and is parallel to the line represented by the equation 2x + 3y = 9. Which of the following equations represents the line?
A line passes through the points (–2,6) and (1,–9). Write its equation in slope-intercept form.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.