Quadratics End of Unit Review

Front

What are the solutions to the equation (x-3)(x+2)=0?

Back

x=3, -2

Front

What is the discriminant of the equation 6x^2 − 2x − 3 = 0?

Back

76

Front

Solve using the quadratic formula: x^2 + 4x - 16 = 0.

Back

x = -2 ± 2√5

Front

Determine the average rate of change of the function f(x) = x^2 - 7x + 8 over the interval -1 ≤ x ≤ 3.

Back

-5

Front

How many seconds does it take the object modeled by f(t) = -5t^2 + 20t + 60 to hit the ground?

Back

6 seconds

Front

What is a quadratic equation?

Back

An equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the vertex of a parabola given by the equation y = ax^2 + bx + c?

Back

The vertex is at the point (-b/(2a), f(-b/(2a))).

Front

What does the discriminant tell us about the roots of a quadratic equation?

Back

If the discriminant (b^2 - 4ac) is positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

What is the standard form of a quadratic function?

Back

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

Front

How do you find the axis of symmetry for a quadratic function?

Back

The axis of symmetry is given by the line x = -b/(2a).