Chapter 3 Test: Quadratics

Front

What is the process to complete the square for a quadratic equation?

Back

To complete the square, divide the 'b' value by 2, square the result, and then add that value to both sides of the equation.

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula \( (-\frac{b}{2a}, f(-\frac{b}{2a})) \) where \( f(x) \) is the quadratic function.

Front

What does the height function h(t) = -16t^2 + 70t + 95 represent?

Back

It models the height of an object thrown into the air, where h(t) is the height in feet after t seconds.

Front

How do you determine if a quadratic equation has real solutions?

Back

Check the discriminant (b^2 - 4ac): if it's positive, there are two real solutions; if zero, one real solution; if negative, no real solutions.

Front

What is the discriminant of a quadratic equation?

Back

The discriminant is the expression \( b^2 - 4ac \) that determines the nature of the roots of the quadratic equation.

Front

What does a negative discriminant indicate about the roots of a quadratic equation?

Back

A negative discriminant indicates that the quadratic equation has no real roots, only complex roots.

Front

How do you evaluate the height of an object at a specific time using the height function?

Back

Substitute the time value into the height function h(t) and solve for h(t).

Front

What is the vertex of the quadratic function represented by the equation y = x^2 + 2x - 3?

Back

The vertex can be found at the point (-1, -4) using the vertex formula.

Front

What is the standard form of a quadratic equation?

Back

The standard form is \( ax^2 + bx + c = 0 \) where a, b, and c are constants.

Front

How do you convert a quadratic equation from standard form to vertex form?

Back

Use the method of completing the square to rewrite the equation in the form \( a(x-h)^2 + k \) where (h, k) is the vertex.