Question

complete the statements.
graph has one real root.
graph has a negative discriminant.
graph has an equation with coefficients
a = 1, b = 4, c = -2

Explanation:

Step1: Identify 1 real root graph

A quadratic with one real root touches the x-axis exactly once. This matches the rightmost graph (Graph A), as it is tangent to the x-axis.

Step2: Identify negative discriminant graph

A negative discriminant means no real roots, so the graph does not intersect the x-axis. This matches Graph C, which is entirely above the x-axis.

Step3: Match coefficients to graph

For quadratic $y=ax^2+bx+c$, $a=1>0$ (opens upward), discriminant: $\Delta = b^2-4ac = 4^2-4(1)(-2)=16+8=24>0$, so two real roots. The vertex x-coordinate is $-\frac{b}{2a}=-\frac{4}{2(1)}=-2$. This matches Graph B, which opens upward, crosses the x-axis twice, and has a vertex at $x=-2$.

Answer:

Graph A has one real root.
Graph C has a negative discriminant.
Graph B has an equation with coefficients $a = 1, b = 4, c = -2$.