How can you tell whether a parabola opens up or opens down by looking at the equation Quizizz?

How can you tell whether a parabola opens up or opens down by looking at the equation? The value of "a" tells you the direction of the opening.

How can you tell whether a parabola opens up or down by looking at the equation?

If the x is squared, the parabola is vertical (opens up or down). If the y is squared, it is horizontal (opens left or right). If a is positive, the parabola opens up or to the right. If it is negative, it opens down or to the left.

Which letter determines if a parabola opens up or down?

Parabolas have a shape that resembles (but is not the same as) the letter U. Parabolas may open upward or downward. If the sign of the leading coefficient, a, is positive (a > 0), the parabola opens upward. If the sign of the leading coefficient, a, is negative (a < 0), the parabola opens downward.

What does it mean when a parabola opens upward or downward?

Whether a parabola opens up or down depends on its equation. If the leading coefficient of a quadratic function is less than zero, the parabola opens downward. If the leading coefficient of a quadratic function is greater than zero, the parabola opens upward.

What does the equation of a parabola look like?

Parabola Equation

The general equation of a parabola is: y = a(x-h)² + k or x = a(y-k)² +h, where (h,k) denotes the vertex. The standard equation of a regular parabola is y² = 4ax.

05 - Graphing Parabolas - Opening Up and Down (Quadratic Equations)

What is the value of a if the graph of a parabola is opens downward?

If a < 0 (negative) then the parabola opens downward. Find the x-intercepts: Notice that the x-intercepts of any graph are points on the x-axis and therefore have y-coordinate 0.

Which quadratic function opens downward and has a vertex?

The quadratic function f(x) = a(x - h)² + k, a not equal to zero, is said to be in standard form. If a is positive, the graph opens upward, and if a is negative, then it opens downward. The line of symmetry is the vertical line x = h, and the vertex is the point (h,k).

Does maximum open up or down?

Vertical parabolas give an important piece of information: When the parabola opens up, the vertex is the lowest point on the graph — called the minimum, or min. When the parabola opens down, the vertex is the highest point on the graph — called the maximum, or max.

What is opening of the graph?

Direction of opening of graph is dependent on the value of. . If a>0 then graph opens upwards and if a<0 then graph opens downwards.

How do you find the direction of opening in factored form?

How do you find the vertex and axis of symmetry?

The axis of symmetry always passes through the vertex of the parabola . The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola. For a quadratic function in standard form, y=ax2+bx+c , the axis of symmetry is a vertical line x=−b2a .

Which parabola opens upward?

In the graph, the highest or lowest point of a parabola is the vertex. The vertex of the graph of y=x2 is (0,0). If a>0 in f(x)=ax2+bx+c, the parabola opens upward. In this case the vertex is the minimum, or lowest point, of the parabola.

How can we determine just by looking at the equation of a parabola whether it has a vertical or a horizontal axis of symmetry?

If the parabola opens up or down, the axis of symmetry is vertical and in this case, its equation is the vertical line that passes through its vertex. If the parabola opens right or left, the axis of symmetry is horizontal and its equation is the horizontal line that passes through its vertex.

What is the direction of parabola with equation y k p?

The directrix is the line y = k - p. The axis is the line x = h. If p > 0, the parabola opens upward, and if p < 0, the parabola opens downward. If a parabola has a horizontal axis, the standard form of the equation of the parabola is this: (y - k)² = 4p(x - h), where p≠ 0.

What is the direction of the graph of quadratic function if the value of A and K are all positive integers?

If the value of the “a” term is positive the parabola will open upward, whereas if the value is negative it opens downward.

How can you tell how big a parabola opens?

The parabola opens downward. In general, use the leading coefficient to determine whether the parabola opens upward or downward. If the leading coefficient is negative, as in the previous example, then the parabola opens downward. If the leading coefficient is positive, then the parabola opens upward.

What is the standard form of the equation of a parabola that opens left or right?

The standard form of a parabola that opens left or right, or a horizontal parabola, is as follows: x = a(y - k)2 + h.