Given the vertex and a point find the equation of a parabola

The video tutorial explains how to find a polynomial with a given vertex and point. It begins by defining a vertex and a point in the context of a parabola. The instructor then introduces the vertex form of a quadratic function and demonstrates how to substitute the vertex into the equation. By using a specific point on the graph, the instructor calculates the value of 'A' in the vertex form. Finally, the tutorial concludes with the derivation of the polynomial equation and explains why the general form does not include specific points.

What is the role of the vertex in a parabola?

• It is the starting point of the parabola.

• It is the point where the parabola intersects the x-axis.

• It is the midpoint of the parabola.

• It is the highest or lowest point of the parabola.

Why is it important to use parentheses when substituting values into the vertex form equation?

• To avoid errors with negative signs.

• To make the equation look neat.

• To simplify the calculation process.

• To ensure the equation is balanced.

How do you determine if a point lies on the graph of a function?

• By checking if the point satisfies the function's equation.

• By plotting the point on the graph.

• By comparing the point to the vertex.

• By calculating the distance from the origin.

What does the vertex form of a parabola equation look like?

• F(x) = A(X + H)^2 + K

• F(x) = A(X - H)^2 - K

• F(x) = A(X + H)^2 - K

• F(x) = A(X - H)^2 + K

What is the purpose of solving for the coefficient 'A' in the vertex form equation?

• To find the x-intercepts of the parabola.

• To determine the direction of the parabola.

• To complete the equation of the parabola.

• To find the y-intercept of the parabola.

Why does the general equation of a parabola not include specific points?

• Because a parabola is defined by its axis of symmetry.

• Because specific points are irrelevant to the equation.

• Because the equation is only concerned with the vertex.

• Because a parabola consists of infinite points.

What is the standard form of the polynomial derived in the video?

• 3 * (X - 2)^2 + 2

• 3 * (X - 2)^2 - 2

• 3 * (X + 2)^2 + 2

• 3 * (X + 2)^2 - 2