Vertex and Equation Forms of Parabolas

The video tutorial explains how to match equations with their corresponding graphs by analyzing the form of the equations. It focuses on two sets of equations: those where the x part is squared and those where the y part is squared. For each set, the tutorial describes how to determine the vertex and the direction in which the parabola opens. The video concludes by matching each equation with the correct graph based on these characteristics.

What is the form of the equation when the x part is squared?

• x = a(y - k)^2 + h

• y = a(x - h)^2 + k

• x = a(y + k)^2 - h

• y = a(x + h)^2 - k

If a parabola opens upwards, what can be said about the value of 'a'?

• a is zero

• a is undefined

• a is negative

• a is positive

For the equation y = 4(x - 3)^2 + 2, what is the vertex?

• (3, -2)

• (3, 2)

• (-3, -2)

• (-3, 2)

Which graph matches the equation y = 4(x + 3)^2 + 2?

• Graph with vertex (-3, -2)

• Graph with vertex (3, 2)

• Graph with vertex (-3, 2)

• Graph with vertex (3, -2)

What is the form of the equation when the y part is squared?

• y = a(x - h)^2 + k

• x = a(y + k)^2 - h

• x = a(y - k)^2 + h

• y = a(x + h)^2 - k

If a parabola opens to the right, what can be said about the value of 'a'?

• a is negative

• a is zero

• a is positive

• a is undefined

For the equation x = 4(y + 2)^2 - 3, what is the vertex?

• (-3, -2)

• (3, 2)

• (-3, 2)

• (3, -2)

Which graph matches the equation x = 4(y - 2)^2 - 3?

• Graph with vertex (3, 2)

• Graph with vertex (-3, -2)

• Graph with vertex (3, -2)

• Graph with vertex (-3, 2)

What is the axis of symmetry for the equation x = a(y - k)^2 + h?

• Vertical

• None

• Diagonal

• Horizontal

In the equation x = 4(y - 2)^2 - 3, what does the constant term represent?

• The axis of symmetry

• The x-coordinate of the vertex

• The y-coordinate of the vertex

• The direction of the parabola