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Fletcher
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How does the second term in a quadratic, bx, affect the graph?
The coefficient b in a quadratic equation, bx, determines the slope of the line in the graph. A positive b value will create an upward sloping parabola, while a negative b value will create a downward sloping parabola.
If b is equal to 0, the quadratic equation becomes y = ax^2, which is a simple parabola with a vertical axis of symmetry. This means the graph will open either upwards or downwards depending on the value of a.
The x-intercepts of a quadratic graph are the points where the graph intersects the x-axis. Changing the value of b will shift the graph horizontally, meaning the x-intercepts will also shift accordingly. For example, if b is increased, the graph will shift to the left, and if b is decreased, the graph will shift to the right.
The vertex of a quadratic graph is the point where the graph reaches its maximum or minimum value. The x-coordinate of the vertex is given by -b/2a, which means that the value of b will directly affect the position of the vertex. A positive b value will shift the vertex to the left, while a negative b value will shift it to the right.
Yes, the value of b can affect the number of solutions to a quadratic equation. If b^2 - 4ac is positive, there will be two distinct solutions to the equation, meaning the graph will intersect the x-axis at two points. If b^2 - 4ac is equal to 0, there will be one solution, and if it is negative, there will be no real solutions.