Midterm Practice #2 ORCA

Front

What is the axis of symmetry for a parabola in standard form?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. For a parabola given by the equation y = ax^2 + bx + c, the axis of symmetry can be found using the formula x = -b/(2a).

Front

Write a system of equations to represent the total number of tickets sold and the total revenue collected from ticket sales.

Back

Let 'a' represent the number of adult tickets and 'c' represent the number of children's tickets. The system of equations is: a + c = 21 (total tickets) and 6a + 4c = 104 (total revenue).

Front

What is the formula used to find the axis of symmetry from the standard form of a quadratic equation?

Back

The formula to find the axis of symmetry from the standard form y = ax^2 + bx + c is x = -b/(2a).

Front

What is the inverse of a matrix?

Back

The inverse of a matrix A is another matrix, denoted as A^(-1), such that when A is multiplied by A^(-1), the result is the identity matrix. Not all matrices have inverses.

Front

If Carolina ran x kilometers on Monday, how many kilometers did she run on Wednesday and Friday?

Back

Carolina ran half as many kilometers on Wednesday as on Monday (x/2) and half as many on Friday as on Wednesday (x/4).

Front

What is the total distance Carolina ran if she ran 8 km on Monday?

Back

If Carolina ran 8 km on Monday, she ran 4 km on Wednesday and 2 km on Friday, totaling 8 + 4 + 2 = 14 km.

Front

Define a quadratic function.

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the vertex of a parabola represent?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether the parabola opens upwards or downwards. It can be found using the formula (h, k) where h = -b/(2a) and k is the value of the function at h.

Front

How do you determine if a quadratic function opens upwards or downwards?

Back

A quadratic function opens upwards if the coefficient 'a' in the standard form y = ax^2 + bx + c is positive, and it opens downwards if 'a' is negative.

Front

What is the significance of the y-intercept in a quadratic function?

Back

The y-intercept of a quadratic function is the point where the graph intersects the y-axis, which occurs when x = 0. It can be found by evaluating the function at x = 0, resulting in the value c in the standard form.