Answer:
3. Completing the Square
4. 0, 1, or 2
Step-by-step explanation:
Hello!
3) Which of the following is NOT a method to find the x-intercepts of a quadratic equation?
a) Graphing
Graphing is a useful method as it lays the answer out in front of you. Once you graph the parabola, you simply take the intersections of the graph and x-axis as your x-intercepts. Therefore, it is a method.
b) Factoring
Factoring can be used to find x-intercepts, and after factoring, you can set each factor to 0 and solve for x, which are the x-intercepts. This method is also called the Zero Product Property.
c) Quadratic Formula
The quadratic formula is meant to solve for the x-intercepts, as the formula uses values of the coefficients to isolate x and solve for it.
Standard form of a Quadratic: [tex]ax^2 + bx + c = 0[/tex]
Quadratic Formula: [tex]x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}[/tex]
Plugging in the values of a, b, and c give you the solutions for x.
d) Completing the Square
Completing the square CAN be used to find the x-intercepts, but not directly so. It is used to convert standard form into a different form, known as the vertex form. It is meant so find the vertex, not the x-intercepts.
Therefore, Completing the Square is NOT a method to find the x-intercepts.
4) How many solutions (x-intercepts) can a quadratic equation have?
The number and types of solutions depend on the discriminant of the quadratic (the part under the square root in the QF).
Types of roots:
- If positive: 2 real roots
- If negative: 2 imaginary roots (technically 0 roots)
- If equal to 0: 1 real root (double root)
That means that a quadratic equation can have 0, 1, or 2 roots.
