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Up or down? X - intercepts?Coordinate of vertex?Line of symmetry ?Y intercept?

Up or down? X - intercepts?Coordinate of vertex?Line of symmetry ?Y intercept?-example-1
User Graywh
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Final answer:

The independent variable is x and the dependent variable is y. The y-intercept is the point where the line intersects the vertical axis. The slope represents the rate of change.

Step-by-step explanation:

The independent variable in this case is represented by the horizontal axis, x. The dependent variable is represented by the vertical axis, y. The y-intercept is the point where the line intersects the vertical axis, and it is denoted by the value of y when x equals zero. The slope of the line represents the rate of change and is determined by how much y changes for a one-unit increase in x.

User Sierra Alpha
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For an equation of a parabola of the form: y = ax² + bx + c we can determine if the parabola opens upward or downward by analyzing the value of the first coefficient "a", if a is a negative number then the parabola opens downwards. We can get an equation of the mentioned form from f(x) = (x + 3)(x - 1) like this:

f(x) = (x + 3)(x - 1) = x² - x + 3x - 3 = x² + 2x - 3

As you can see, a equals 1, then the parabola opens upward

The x-intercepts of the function can be determined by calculating the values that make f(x) to be equal to 0, by replacing -3 and 1 for x into the function f(x) = (x + 3)(x - 1) you can easily prove that the x-intercepts are -3 and 1.

The coordinates of the vertex can be calculated by means of the following formula:


((-b)/(2a),f((-b)/(2a)))

In this case, b equals 2 and a equals 1, by replacing these values into -b/2a, we get:


xv=(-2)/(2\cdot1)=(-2)/(2)=-1

By replacing -1 for x into f(x), we get:

f(x) = ((-1) + 3)((-1) - 1) = (2)(-2) = - 4

Then, the coordinates of the vertex are (-1, -4)

The line of symmetry is a vertical line that passes through the vertex and has the form x = v, where v is the x-coordinate of the vertex. in this case, v equals -1, then the line of symmetry should be:

x = -1

The y-intercept of a parabola can be calculated by replacing 0 for x into the formula of f(x), then we get:

f(0) = (0 + 3)(0 - 1) = (3)(-1) = -3

Then, the y-intercept of the parabola equals -3

User EdwinW
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