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For standard form: y=Ax^2+Bx+C. Look at the coefficient of the x^2 term. If "A" is positive, the parabola opens up. If "A" is negative, then the parabola opens down. For Vertex Form: y=a (x-h)^2+k. The sign of "a" determines the direction of the parabola. If "a" is positive, the parabola opens up.
Convert y = 3x 2 + 9x + 4 to vertex form: y - 4 = 3x 2 + 9x. y - 4 = 3(x 2 + 3x) y - 4 + 3(?) = 3(x 2 + 3x + ?) y - 4 + 3() = 3(x 2 + 3x + ) y - = 3(x + ) 2. y = 3(x + ) 2 - This is our equation in vertex form, which tells us that the vertex is at (, ), and also that our parabola opens upwards, since a (3 in this case) is positive.
While the standard quadratic form is $ax^2+bx+c=y$, the vertex form of a quadratic equation is $\bi y=\bi a(\bi x-\bi h)^2+ \bi k$. In both forms, $y$ is the $y$-coordinate, $x$ is the $x$-coordinate, and $a$ is the constant that tells you whether the parabola is facing up ($+a$) or down ($-a$).
Jan 18, 2024 · The vertex form is y = a(x - 2)² + 5, where a is the same non-zero parameter as in the standard form. For each value of a , you get a different parabola, so you need to specify a to get a definite result.
Jun 4, 2023 · This is the advantage of vertex form. The transformations required to draw the graph of the function are easy to spot when the equation is written in vertex form. It’s a simple matter to transform the equation f(x) = (x + 2)2 + 3 into the general form of a quadratic function, f(x) = ax2 + bx + c.
The vertex form of a quadratic function is given by. f (x) = a(x - h)2 + k, where (h, k) is the vertex of the parabola. Remember: the "vertex? is the "turning point". When written in " vertex form ": • (h, k) is the vertex of the parabola, and x = h is the axis of symmetry.
