Midterm exam review 2024

Front

What is the simplified form of \( \frac{-10+6i}{17} \)?

Back

The simplified form is \( \frac{1+50i}{61} \).

Front

Given \( f(x) = 3x + 10 \) and \( g(x) = x - 2 \), what is \( f(g(0)) \)?

Back

The value of \( f(g(0)) \) is 4.

Front

Describe the transformations of the function \( -g(x) + 2 \).

Back

The function is reflected across the x-axis and shifted 2 units up.

Front

What is \( f(0) \) if \( f(x) = 3x - 2 \)?

Back

The value of \( f(0) \) is -2.

Front

Convert the quadratic function \( f(x) = x^2 + 10x + 24 \) to vertex form.

Back

The vertex form is \( f(x) = (x + 5)^2 - 1 \).

Front

What is the vertex of the parabola represented by \( f(x) = x^2 + 10x + 24 \)?

Back

The vertex is at the point (-5, -1).

Front

What does it mean to reflect a function across the x-axis?

Back

Reflecting a function across the x-axis means to invert the sign of the output values.

Front

What is the standard form of a quadratic function?

Back

The standard form is \( f(x) = ax^2 + bx + c \).

Front

How do you find the x-intercepts of a quadratic function?

Back

Set \( f(x) = 0 \) and solve for \( x \).

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant determines the nature of the roots: positive for two real roots, zero for one real root, and negative for two complex roots.