Question

HELP Please!!!

What statements are true about the quadratic equation?


The value of a is negative in the equation y = ax 2 + bx + c. TRUE or FALSE

The vertex of the graph is the point (-1, 3). TRUE or FALSE

The equation of the axis of symmetry is x = 3. TRUE or FALSE

Answer 1

False

False

True

Explanation:

Since it's a concave up, a > 0

Vertex: (3,-1)

Symmetry: x = 3

Answer 2

1. false

2. false

3. true

Explanation:

1. If the value of a was negative, then the graph of the quadratic would open downwards because the negative sign would induce a reflection of the graph over the x-axis.

However, we can see from the graph that the quadratic opens up, so a is not negative and this statement is false.

2. The vertex of a quadratic equation is the minimum or maximum point. Here, since the graph points up, the vertex will be the minimum point. That point is actually (3, -1). Clearly, this is not (-1, 3), so the statement is false.

3. The axis of symmetry is essentially the line with the x-value of the vertex. Since the x-coordinate of the vertex is 3, that means the axis of symmetry is the line x = 3. Thus, the statement is true.