Study Group 3/26/2025

Complete the Square

100

What is the first step to completing the square?

Divide the factor b by two.

200

Solve by completing the square:
x²+14x=24

x=-7+-sqrt73

300

Solve by completing the square:
2x²-1=3x

x=(3+-sqrt17)/4

400

How do you know whether to add or subtract when you're completing the square?

When they're on the same side, you add and subtract. When on different sides, add to both sides.

Quadratics

100

What is the axis of symmetry?

x=h

200

What is the standard form of a quadratic?

ax²+bx+c

300

How do you know whether a quadratic has a max or min?

a<0 is a max, a>0 is a min.

400

What is the max or min of any given quadratic?

k

Formulas

100

What is the quadratic formula?

(-b+-(sqrtb²-4ac))/2a

200

What is vertex form?

a(x-h)²+k

300

How do you find h, the x-value of the vertex?

-b/2a

400

How do you find k, the y-value of the vertex?

k(-b/2a) or k(h)

Polynomial Functions & Inequalities

100

What is the standard form of a polynomial?

(a_nxⁿ...a₀)

200

What is the degree of a polynomial?

The largest exponent (n)

300

What differentiates the leading term and the leading coefficient?

The leading term is the FULL term (a_nxⁿ) with the largest exponent whereas the leading coefficient is JUST the coefficient (a_n)

400

What is the constant term?

The term in the polynomial with no x value.