I think not. First off, that's not an equation. Second, the axis of symmetry is the line y = 0 (the x-axis). This means that the equation will be x = ay^2 + by + c.jOANIE said:Homework Statement
Write the equation in standard form for the parabola with an axis of symmetry y=0 and focus(-5,0).
Homework Equations
I think ax^2+bx+c.
x = -b/(2a) isn't the equation of a parabola; it gives you the x-coordinate of the vertex for a parabola that opens up or down. Your parabola opens left or right.jOANIE said:Also maybe x = -b/2a. But I don't know how to apply these.
jOANIE said:The Attempt at a Solution
I know that focus and vertex lie on axis of symmetry and that directrix ane axis of symmetry are perpendicular to each other.
If you could give me a similar example worked out, I would be able to do this one. Thanks.
The standard form of the equation of a parabola is y = ax^2 + bx + c, where a, b, and c are constants and a is not equal to 0.
The value of a in the standard form equation determines the direction and shape of the parabola. If a is positive, the parabola opens upwards and has a "U" shape. If a is negative, the parabola opens downwards and has an "n" shape.
The constant b represents the horizontal shift of the parabola, while the constant c represents the vertical shift. If b is positive, the parabola shifts to the left, and if b is negative, the parabola shifts to the right. Similarly, if c is positive, the parabola shifts upwards, and if c is negative, the parabola shifts downwards.
To graph a parabola using the standard form equation, you can use the x-intercepts and y-intercept. The x-intercepts are where the parabola crosses the x-axis, and they can be found by setting y to 0 and solving for x. The y-intercept is where the parabola crosses the y-axis, and it can be found by setting x to 0 and solving for y. Once you have the intercepts, you can plot them on a graph and draw a smooth curve connecting them to create the parabola.
The standard form and vertex form are two different ways of writing the equation of a parabola. The standard form y = ax^2 + bx + c shows the parabola in its general form, while the vertex form y = a(x-h)^2 + k shows the parabola in its vertex form. The constants h and k represent the coordinates of the vertex of the parabola.