How does the graph of y x 2 differ from the graph of y x 2 4?

y=x2 is the Parent Graph. y=x2+4 is the graph of the given function. If the coefficient of the x-term (a) is positive, the graph of the parabola Opens Up.

How is the graph of y x 2 3 different from the graph of y x 2?

Graphing y = (x – h)2 + k In a parabola that opens downward, the vertex is the maximum point. We can graph a parabola with a different vertex. Observe the graph of y = x2 + 3: Graph of y = x2 + 3 The graph is shifted up 3 units from the graph of y = x2, and the vertex is (0, 3).

Which equation describes the graph y x 2 y x 2 y x 2?

The equation of the axis of symmetry for the graph of y=ax2+bx+c. Substitute −3 for a and −5 for b in the equation of the axis of symmetry. So, the equation of the axis of symmetry is x=−1. Since the equation of the axis of symmetry is x=−1 and the vertex lies on the axis, the x-coordinate of the vertex is −1.

What is the vertex of y x 2 4?

Therefore, the vertex is at (0,−4) .

How do the values of H and K in Y a XH 2 K affect the graph of y ax2?

When written in “vertex form”: (h, k) is the vertex of the parabola, and x = h is the axis of symmetry. the h represents a horizontal shift (how far left, or right, the graph has shifted from x = 0). the k represents a vertical shift (how far up, or down, the graph has shifted from y = 0).

What is equation and inequalities?

Equations and inequalities are both mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are deemed equal which is shown by the symbol =. An equation or an inequality that contains at least one variable is called an open sentence. …

What is the slope of the equation y x 2 )+ 8?

The slope, m , is 4 .

How does the value of a affect the graph of y ax 2?

When the value of “a” is a less than 0, the graph of the function is a reflection across the x-axis of the original function. The parabola gets narrower or wider depending on the value of “a.”