PLEASE HELP ME QUICKKK, FIRST CORRECT PERSON GETS BRAINLIEST
1 answer:
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Answer:
1) Point -----> see the attached figure N
2) The value of x is
3) I quadrant
4)
5)
Step-by-step explanation:
Part 1)
we know that
If the point satisfy the inequality
then
the point must be included in the shaded area
The point is included in the shaded area
Part 2)
we have
see the attached figure N
we know that
The value for x on the boundary line and the x axis is equal to the x-intercept of the line
For
Find the value of x
The solution is
Part 3)
we have
-----> inequality A
The solution of the inequality A is in the first and fourth quadrant
-----> inequality B
The solution of the inequality B is in the first and second quadrant
so
the solution of the inequality A and the inequality B is the first quadrant
Part 4) Which ordered pair is a solution of the inequality?
we have
we know that
If a ordered pair is a solution of the inequality
then
the ordered pair must be satisfy the inequality
we're going to verify all the cases
<u>case A)</u> point
Substitute the value of x and y in the inequality
------> is not true
therefore
the point is not a solution of the inequality
<u>case B)</u> point
Substitute the value of x and y in the inequality
------> is not true
therefore
the point is not a solution of the inequality
<u>case C)</u> point
Substitute the value of x and y in the inequality
------> is not true
therefore
the point is not a solution of the inequality
<u>case D)</u> point
Substitute the value of x and y in the inequality
------> is true
therefore
the point is a solution of the inequality
Part 5) Write an inequality to match the graph
we know that
The equation of the line has a negative slope
The y-intercept is the point
The x-intercept is a positive number
The solution is the shaded area above the dashed line
so
the equation of the line is
The inequality is
Answer:
Axis is a vertical line at x = 2
Vertex is (2, -1)
y-intercept is (0, 3)
Solutions are x = 1 and x = 3
Step-by-step explanation:
To draw the graph of the quadratic equation you must find at least 5 points lie on the graph by choose values of x and find their values of y
Let us do that
Use x = -1, 0, 1, 2, 3, 4, 5
∵ y = x² - 4x + 3
∵ x = -1
∴ y = (-1)² - 4(-1) + 3 = 1 + 4 + 3 = 8
→ Plot point (-1, 8)
∵ x = 0
∴ y = (0)² - 4(0) + 3 = 0 + 0 + 3 = 3
→ Plot point (0, 3)
∵ x = 1
∴ y = (1)² - 4(1) + 3 = 1 - 4 + 3 = 0
→ Plot point (1, 0)
∵ x = 2
∴ y = (2)² - 4(2) + 3 = 4 - 8 + 3 = -1
→ Plot point (2, -1)
∵ x = 3
∴ y = (3)² - 4(3) + 3 = 9 - 12 + 3 = 0
→ Plot point (3, 0)
∵ x = 4
∴ y = (4)² - 4(4) + 3 = 16 - 16 + 3 = 3
→ Plot point (4, 3)
∵ x = 5
∴ y = (5)² - 4(5) + 3 = 25 - 20 + 3 = 8
→ Plot point (5, 8)
→ Join all the points to form the parabola
From the graph
∵ The axis of symmetry is the vertical line passes through the vertex point
∵ x-coordinate of the vertex point is 2
∴ Axis is a vertical line at x = 2
∵ The coordinates of the vertex point of the parabola are (2, -1)
∴ Vertex is (2, -1)
∵ The parabola intersects the y-axis at point (0, 3)
∴ y-intercept is (0, 3)
∵ x² - 4x + 3 = 0
∵ The solutions of the equation are the values of x at y = 0
→ That means the intersection points of the parabola and the x-axis
∵ The parabola intersects the x-axis at points (1, 0) and (3, 0)
∴ Solutions are x = 1 and x = 3
