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I really am bad with math and just have given up

With trying to solve these equations can someone help

I really am bad with math and just have given up With trying to solve these equations-example-1

1 Answer

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well hmmm does the graph open upwards or downwards? well
is a quadratic, if the leading term's coefficient is negative, Down, if positive, Up

a)
now, let's see the leading term, -x², what's its coefficient? is -1 * x² or -1x², is -1, so is negative, thus is opening downwards

c)
x-intercepts occur, when y = 0, namely y = -x²-4x-3, so setting y to 0
0 = -x² -4x -3 take a common factor of -1, thus

0 = -1 (x²+4x+3) <--- now, if we factor that out, notice, surely you've done many of these by now, so we end up with


\bf \begin{array}{lcclll} 0=x^2&amp;+4x&amp;+3\\ &amp;\uparrow &amp;\uparrow \\ &amp;3+1&amp;3\cdot 1 \end{array}\\\\ -----------------------------\\\\ 0=(x+3)(x+1)\implies \begin{cases} 0=x+3\implies &amp;-3=x\\ 0=x+1\implies &amp;-1=x \end{cases}

so, the x-intercepts are at -3 and -1

d)

now, the y-intercepts, just set x = 0
y = -x²-4x-3, settting x to 0 y = -0²-4(0)-3, which is y = -3

so the sole y-intercept is at y = -3


now, let's get on to b)

b)
\bf \textit{vertex of a parabola}\\\\ \begin{array}{lccclll} f(x)=&amp;-1x^2&amp;-4x&amp;-3\\ &amp;\uparrow &amp;\uparrow &amp;\uparrow \\ &amp;a&amp;b&amp;c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)

and those are the coordinates, notice a = -1, b = -4 and c = -3

now, for

e)

well, all you have to do is, once you have the vertex, pick an x-value on the left-hand-side of the vertex, get they value for "y", or OUTPUT,

then pick another x-value, on the right-hand-side of the vertex, get the "y" value again, and plot away
User Vineet Goel
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