Solve the two-step equation.− 23 x – 214 = 274x =
2 answers:
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Answer:
The line of symmetry is x = -3
Explanation:
Given a quadratic function, we know that the graph is a parabola. The general form of a parabola is:
The line of symmetry coincides with the x-axis of the vertex. To find the x-coordinate of the vertex, we can use the formula:
In this problem, we have:
Then:
a = -1
b = -6
We write now:
For this part, we need to find the x-intercepts. This is, when y = 0:
To solve this, we can use the quadratic formula:
And solve:
Since there is no solution to the square root of a negative number, the function does not have any x-intercept. The correct option is ZERO x-intercepts.
Part 4:
To find the y intercept, we need to find the value of y when x = 0:
The y-intercept is at (0, -13)
Part 5:
Now we need to find two points in the parabola. Let-s evaluate the function when x = 1 and x = -1:
The two points are:
(1, -20)
(-1, -8)
Part 6:
Now, we can use 3 points to find the graph of the parabola.
We can locate (1, -20) and (-1, -8)
The third could be the vertex. We need to find the y-coordinate of the vertex. We know that the x-coordinate of the vertex is x = -3
Then, y-coordinate of the vertex is:
The third point we can use is (-3, -4)
Now we can locate them in the cartesian plane:
And that's enough to get the full graph:
