y=2(x-3)+1
Assuming the vertex is 0,0 and the directrix is y=4 x^2=0
To determine if ( y = (x - 1)(x - 3) ) is an equation for a parabola, we can rewrite it in standard form. Expanding this gives ( y = x^2 - 4x + 3 ), which is indeed a quadratic equation representing a parabola. Therefore, yes, ( y = (x - 1)(x - 3) ) is an equation for a parabola.
To find the vertex of a quadratic equation in standard form, (y = ax^2 + bx + c), you can use the vertex formula. The x-coordinate of the vertex is given by (x = -\frac{b}{2a}). Once you have the x-coordinate, substitute it back into the equation to find the corresponding y-coordinate. The vertex is then the point ((-\frac{b}{2a}, f(-\frac{b}{2a}))).
when the function is in vertex form: y = a(x - h)2 + k, the point (h, k) is the vertex.
The graph of a quadratic function is always a parabola. If you put the equation (or function) into vertex form, you can read off the coordinates of the vertex, and you know the shape and orientation (up/down) of the parabola.
The vertex form for a quadratic equation is y=a(x-h)^2+k.
-2
Normally a quadratic equation will graph out into a parabola. The standard form is f(x)=a(x-h)2+k
An equation that when plotted produces a parabola is a quadratic equation of the form y = ax2 + bx + c where a, b and c are constants.
please help
A linear equation has the form of mx + b, while a quadratic equation's form is ax2+bx+c. Also, a linear equation's graph forms a line, while a quadratic equation's graph forms a parabola.
2
y=2(x-3)+1
It is a quadratic equation that normally has two solutions
The vertex form of a quatdratic equation (otherwise called the graphing form) is y=a(x-h)2+k For those of you who don't know what 'h', 'a', and 'k' are, they are parameters. The negative sign in front of the 'h' refers to the opposite of the x coordinate in the vertex. The 'k' refers to the y coordinate in the vertex. 'A' refers to the stretch or compression factor. So, for example, say you have a parabola with a stretch factor of 2 whose vertex coordinates are (-3,4). The equation would be y=2(x+3)2+4 Of course, if a parabola has no stretch/compression factor, there would be no 'a' in the equation. I hope this helped, and good luck!
The difference between standard form and vertex form is the standard form gives the coefficients(a,b,c) of the different powers of x. The vertex form gives the vertex 9hk) of the parabola as part of the equation.