Systems of Quadratics

Front

What are the possible number of solutions for the intersection of a line and a parabola?

Back

No solutions, 1 solution, or 2 solutions.

Front

What is the solution to the linear-quadratic function represented by the point (2, -3)?

Back

(2, -3) is the solution.

Front

Which point is a solution to the system of equations graphed on the axes?

Back

(8, 9) is a solution.

Front

What are the solutions to the system of equations represented by the points (1, -1) and (4, 2)?

Back

(1, -1) and (4, 2) are the solutions.

Front

How do you determine when two objects described by quadratic equations will pass each other?

Back

Set the equations equal to each other and solve for x.

Front

What is the general form of a quadratic equation?

Back

y = ax^2 + bx + c, where a, b, and c are constants.

Front

What does the vertex of a parabola represent?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

How can you find the x-intercepts of a quadratic function?

Back

Set y = 0 and solve the equation ax^2 + bx + c = 0.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b^2 - 4ac) determines the number of real solutions: if >0, two solutions; =0, one solution; <0, no real solutions.

Front

What is the axis of symmetry in a parabola?

Back

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