SEMESTER 1 FINALS (ALGEBRA 2A)

Front

What is the result of multiplying \( (x+5)(x^2+3x+5) \)?

Back

The result is \( x^3 + 8x^2 + 20x + 25 \).

Front

What are the solutions to the equation \( j(j-9)=0 \)?

Back

The solutions are \( j=0 \) and \( j=9 \).

Front

What are the solutions to the equation \( (u-2)(u+8)=0 \)?

Back

The solutions are \( u=2 \) and \( u=-8 \).

Front

Identify the value of \( c \) in the quadratic equation \( y=16x^2-8x-24 \).

Back

The value of \( c \) is \( -24 \).

Front

Determine the values of \( a, b, \) and \( c \) for the quadratic equation \( 4x^2-8x=3 \).

Back

The values are \( a=4, b=-8, c=-3 \).

Front

What is the standard form of a quadratic equation?

Back

The standard form is \( ax^2 + bx + c = 0 \).

Front

How do you find the vertex of a quadratic function?

Back

The vertex can be found using the formula \( \left( -\frac{b}{2a}, f\left(-\frac{b}{2a}\right) \right) \).

Front

What is the quadratic formula?

Back

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

Front

What does the discriminant of a quadratic equation tell you?

Back

The discriminant \( b^2 - 4ac \) indicates the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

Front

What is the factored form of a quadratic equation?

Back

The factored form is \( a(x - r_1)(x - r_2) \), where \( r_1 \) and \( r_2 \) are the roots.