Question

Between which two ordered pairs does the graph of f(x) = one-halfx2 + x – 9 cross the negative x-axis?

Answer 1

Answer:

its a (-6,0) and (-5,0)

Step-by-step explanation:

Answer 2

None of Option are correct

Step-by-step explanation:

The Given function is f(x) = y = $\frac{1}{2} x^{2} + x -9$

Here, f(x) is quadratic function and it asked that when function cross the Negative X-axis.

If any function cross the X-axis then, Point of intersection will have y component as zero.

Therefore, f(x) = y = $\frac{1}{2} x^{2} + x -9$

y = $\frac{1}{2} x^{2} + x -9 = 0$

Solving quadratric equation,

Comparing with $ax^{2} + bx + c= 0$

We get a=$\frac{1}{2}$, b=1, c=(-9)

Since,

$x=\frac{-b+\sqrt{b^{2}-4ac } }{2a}$

$x=\frac{- 1+\sqrt{(1)^{2}-4(\frac{1}{2})(-9) }}{2(\frac{1}{2})}$

$x=\frac{-1+\sqrt{1+(2)(9)}}{1}$

$x=\frac{-1+\sqrt{19}}{1}$

$x=-1+\sqrt{19}and x=-1-\sqrt{19}$

Thus, None of option are correct.

Verification.....

A) (–6, 0) and (–5, 0) give quadratic function : y = $x^{2} + 11x +30$

B) (–4, 0) and (–3, 0) give quadratic function : y = $x^{2} + 7x +12$

C) (–3, 0) and (–2, 0) give quadraric function : y = $x^{2} + 5x +6$

D) (–2, 0) and (–1, 0) give quadratic function : y = $x^{2} + 3x +2$