# Write an equation in standard form of the parabola whose equation

Divide each side by 2. Use the equation found in part a to find the depth of the fire starter. In this example, let the point be 3, 8. Solve for a Solve the equation for a. The parabola opens downward, because the value of 4a, the multiplier on the right, is The answer is equation: vertex: —3, 2 ; opens to the right.

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So when examining the coefficient of x2, we are examining a. The vertex of the parabola is 8, —3.

### Find the standard form of the equation of the parabola with the given characteristics

Substitute in Coordinates for the Vertex Substitute the vertex's coordinates for h and k in the vertex form. Assume that the vertex of the parabolic mirror is the origin of the coordinate plane. Find the equation of the parabola that models the fire starter. Let's take a look. For ANY point on a parabola, the distance from that point to the focus is the same as the distance from that point to the directrix. Complete the square on the left by moving the y and 4 to the right side and adding 9 to each side of the equation. Move the x and 9 to the right. The answer is equation: vertex: —2, 5 ; opens downward. You worked with parabolas in Algebra 1 when you graphed quadratic equations. Tips Set either form to zero and solve the equation to find the points where the parabola crosses the x-axis. Keep in mind that all information you already know about parabolas remains true! Try It Balcony-sized solar cookers have been designed for families living in India.

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