Question

Someone please helpppp

Answer 1

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: $ax^2 + bx + c = 0$

Quadratic Formula: $x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}$

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.