3.4 Practice (Quad. Formula)

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What are the values of a, b, and c in the equation 4x² - 8x = 3?

Back

a = 4, b = -8, c = -3.

Front

How do you use the quadratic formula to solve a quadratic equation?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a). You substitute the values of a, b, and c from the equation into this formula.

Front

What is the discriminant in the quadratic formula, and what does it indicate?

Back

The discriminant is the part of the quadratic formula under the square root: b² - 4ac. It indicates the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

What is the first step in solving the equation x² + 6x - 13 = 3?

Back

The first step is to make it equal to 0 by subtracting 3 from both sides, resulting in x² + 6x - 16 = 0.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

In the equation y = x² + 5x + 7, what are the values of a, b, and c?

Back

a = 1, b = 5, c = 7.

Front

What does it mean for a quadratic equation to be in vertex form?

Back

A quadratic equation is in vertex form when it is expressed as y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How can you determine if a quadratic equation opens upwards or downwards?

Back

A quadratic equation opens upwards if the leading coefficient (a) is positive and downwards if it is negative.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).