ok, I totally did not get this question at all.
Complete each statement. Assume the variable a does not equal 0.
a. The graph of y=ax^2+c intersects the x-axis in two places when ______.
b. The graph of y=ax^2+c does not intersect the x-axis when ______.
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Plz somebody explain this to me. Any help is greatly appreciated!!!
This equation is a parabola. In order for it to intersect the x-axis in 2 places, the bottom point of the parabola has to be below the x-axis. Therefore, the point c, which is the minimum of the parabola (where x is 0) has to be less than 0. If c is >0, then it does not cross the x-axis, because the whole graph sits above the x-axis.
oh, i get it now!!! Thanx so so much! You guys help me out a lot!
y=-4x^2
I'm glad you were able to understand the question with the explanation provided. If you ever come across similar questions, here's how you can approach solving them:
a. The graph of y = ax^2 + c intersects the x-axis in two places when the value of c is less than zero. This is because a parabola opens upwards when a is positive, and if c is negative, it shifts the parabola downward, allowing it to intersect the x-axis at two distinct points.
To get this answer, you need to understand the properties of quadratic functions. In a quadratic equation in the form y = ax^2 + bx + c, the graph is a parabola. The value of a determines the direction the parabola opens (upwards or downwards), and c represents the y-coordinate of the vertex (minimum or maximum point) of the parabola.
b. The graph of y = ax^2 + c does not intersect the x-axis when the value of c is greater than or equal to zero. If c is greater than zero, it shifts the parabola upward, causing it to lie entirely above the x-axis, meaning it won't intersect it. In case c equals zero, the parabola would touch the x-axis at the vertex, but it wouldn't cross it.
To understand this, it's helpful to visualize the graph of a parabola and how it changes with different values of c. You can also use tools such as graphing calculators or graphing software to plot the functions and see how they behave.
Remember, in order to understand these concepts better, it's important to practice more examples and get familiar with solving quadratic equations and graphing parabolas.