EOC Review "Fundamentals"

Front

What are the zeros of a quadratic equation?

Back

The zeros of a quadratic equation are the values of x that make the equation equal to zero. For example, in the equation (x+10)(x-2) = 0, the zeros are x = -10 and x = 2.

Front

How do you determine the number of solutions for a quadratic equation using the discriminant?

Back

The discriminant is calculated using the formula b² - 4ac. If the discriminant is positive, there are two solutions; if it is zero, there is one solution; if it is negative, there are no real solutions.

Front

What is the formula for the discriminant?

Back

The formula for the discriminant is b² - 4ac.

Front

What does it mean if the discriminant is positive?

Back

If the discriminant is positive, it means the quadratic equation has two distinct real solutions.

Front

What does it mean if the discriminant is zero?

Back

If the discriminant is zero, it means the quadratic equation has exactly one real solution (a repeated root).

Front

What does it mean if the discriminant is negative?

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If the discriminant is negative, it means the quadratic equation has no real solutions (the solutions are complex).

Front

How do you solve a system of equations by elimination?

Back

To solve by elimination, manipulate the equations to eliminate one variable by adding or subtracting the equations. This often involves multiplying one or both equations by a constant.

Front

What is the solution to the system of equations 4x - 6y = -6 and -2x - 12y = -12?

Back

The solution is (0, 1).

Front

How do you find the zeros of the equation (x+10)(x-2) = 0?

Back

Set each factor equal to zero: x + 10 = 0 gives x = -10, and x - 2 = 0 gives x = 2. Thus, the zeros are -10 and 2.

Front

What are the steps to solve a quadratic equation using the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a). Identify a, b, and c from the equation ax² + bx + c = 0, calculate the discriminant, and then apply the formula.