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What happens to the graph when your B term gets bigger in quadratic function?
Assuming that the B term is the linear term, then as B increases, the graph with a positive coefficient for the squared term shifts down and to the left. This means that a graph with no real roots acquires real roots and then the smaller root approaches -B while the larger root approaches 0 so that the distance between the roots also approaches B. The minimum value decreases.
A quadratic function is a function whose rule is a polynomial of degree what?
Oh honey, a quadratic function is a function whose rule is a polynomial of degree 2. It's like the middle child of polynomials - not too simple, not too complex, just right. So next time you see that squared term, you know you're dealing with a quadratic function, sweetie.
How to tell if there are no real roots?
The real roots of what, exactly? If you mean a square trinomial, then: If the discriminant is positive, the polynomial has two real roots. If the discriminant is zero, the polynomial has one (double) real root. If the discriminant is negative, the polynomial has two complex roots (and of course no real roots). The discriminant is the term under the square root in the quadratic equation, in other words, b2 - 4ac.
How can a quadratic function have both a maximum and a minimum point?
A quadratic function can only have either a maximum or a minimum point, not both. The shape of the graph, which is a parabola, determines this: if the parabola opens upwards (the coefficient of the (x^2) term is positive), it has a minimum point; if it opens downwards (the coefficient is negative), it has a maximum point. Therefore, a quadratic function cannot exhibit both extreme values simultaneously.
How is the constant term of a quadratic function related to the y-intercept of its graph?
It is the y-coordinate of the intercept (the x-coordinate being 0).
