Semester 1 Review Day 4

Front

Identify the 'c' value in the quadratic equation: y = 16x^2 - 8x - 24

Back

The 'c' value is -24.

Front

What is the quadratic formula used to solve equations of the form ax^2 + bx + c = 0?

Back

The quadratic formula is x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}.

Front

Solve the equation using the quadratic formula: 5x^2 - 6 = 13x

Back

The solutions are x = 3 and x = -\frac{2}{5}.

Front

What is the simplified form of (–6i)(3i)?

Back

The simplified form is 18.

Front

Simplify the expression: (5x – 2i) + (–7x + 8i)

Back

The simplified expression is -2x + 6i.

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax^2 + bx + c = 0, where a, b, and c are constants.

Front

What does the discriminant (b^2 - 4ac) tell us about a quadratic equation?

Back

The discriminant determines the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form is y = a(x - h)^2 + k, where (h, k) is the vertex.

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula h = -\frac{b}{2a} and then substituting h back into the equation to find k.

Front

What is the result of multiplying two imaginary numbers, such as (3i)(4i)?

Back

The result is -12, since i^2 = -1.