Sketch the graph of the equation. $$y = - 4 x ^ { 2 } + 5$$

Question

Quizplus · Accepted Answer

The given equation is a quadratic equation with a negative coefficient of the squared term. This indicates that the graph is a downward-facing parabola.

The constant term, 5, indicates that the vertex of the parabola is at (0,5).

To sketch the graph, we can also find the horizontal intercepts and the axis of symmetry.

To find the horizontal intercepts, we set y = 0 and solve for x:
$$0 = -4x^2 + 5$$
$$4x^2 = 5$$
$$x^2 = \frac{5}{4}$$
$$x = \pm \frac{\sqrt{5}}{2}$$

So the horizontal intercepts are approximately (-0.79,0) and (0.79,0).

The axis of symmetry passes through the vertex and is a vertical line. In this case, it is the line x = 0.

Using this information, we can sketch the graph as shown in choice (B).

Sketch the Graph of the Equation y=−4x2+5y = - 4 x ^ { 2 } + 5y=−4x2+5

Sketch the Graph of the Equation $y = - 4 x ^ { 2 } + 5$