Write equations of parabolas in vertex form using properties

Learning Objectives Identify the vertex (h, k) and another point (x, y) on a parabola from a graph or description. Distinguish between the vertex form equations for vertical and horizontal parabolas. Substitute the coordinates of the vertex and a point into the appropriate vertex form equation. Algebraically solve for the value of 'a', which determines the parabola's stretch and direction. Write the final equation of a vertical parabola in the form y = a(x - h)^2 + k. Write the final equation of a horizontal parabola in the form x = a(y - k)^2 + h. Determine the direction a parabola opens based on its equation. Ever wondered how a satellite dish perfectly focuses signals to one point, or the beautiful arc a basketball makes on its way to the hoop? 🏀 That pe...

TermDefinitionExample ParabolaA U-shaped curve where any point is at an equal distance from a fixed point (the focus) and a fixed line (the directrix).The path of a ball thrown into the air. VertexThe highest, lowest, or furthest point on a parabola, representing its turning point. It is denoted by the coordinates (h, k).For a parabola that opens upwards, the vertex is the minimum point, like the bottom of a valley. Axis of SymmetryA line that passes through the vertex and divides the parabola into two perfect mirror images.For a parabola with vertex (3, 4) that opens up or down, the axis of symmetry is the vertical line x = 3. Vertex Form (Vertical)The standard equation for a parabola that opens upwards or downwards: y = a(x - h)^2 + k.The equation y = 2(x - 1)^2 + 5 represents a parabol...

Vertex Form for a Vertical Parabola y = a(x - h)^2 + k Use this form when the parabola opens up or down. (h, k) is the vertex. If a > 0, the parabola opens upwards. If a < 0, the parabola opens downwards. Vertex Form for a Horizontal Parabola x = a(y - k)^2 + h Use this form when the parabola opens left or right. (h, k) is the vertex. If a > 0, the parabola opens to the right. If a < 0, the parabola opens to the left. Note that h is the x-coordinate and k is the y-coordinate of the vertex, but their positions in the formula are swapped compared to the vertical form.