Which graph represents a quadratic function that has one real zero?

Mathematics

1 answer:

denis23 [38]3 years ago

6 0

Answer:

Quadratic functions have equations that have two solutions. However, there are specific cases where one answer can be non-real, that is, a complex solution. When that happens, it means the graph of the function has only one x-intercept point.

In this case, the graph that has one real zero is attached. Observe that the parabolla has only one point which intercepts with x-axis, that's the unique real zero.

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now, to get the y-intercept, we simply set x = 0 and solve for y, and to get the x-intercept, we set y = 0 and solve for x.

$\bf \stackrel{\textit{y-intercept, x = 0}}{y+5=\cfrac{2}{7}(0)-4}\implies y+5=-4\implies y=-9\qquad \qquad \stackrel{y-intercept}{(0~,-9)}\\\\ -------------------------------\\\\ \stackrel{\textit{x-intercept, y = 0}}{(0)+5=\cfrac{2}{7}x-4}\implies 5=\cfrac{2x}{7}-4\implies 9=\cfrac{2x}{7}\implies 63=2x \\\\\\ \cfrac{63}{2}=x\implies 31\frac{1}{2}=x\qquad \qquad \qquad \qquad \qquad \qquad \qquad \stackrel{x-intercept}{\left( 31\frac{1}{2}~,~0 \right)}$

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