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Y_Kistochka [10]
3 years ago
15

How do I write the equation of the parabola in intercept form​

Mathematics
1 answer:
lord [1]3 years ago
8 0

Answer:

The equation of the parabola in intercept form is y = -\frac{3}{4}\cdot x\cdot (x-4).

Step-by-step explanation:

The equation of the parabola in intercept form is defined by following formula:

y = a\cdot (x-r_{1})\cdot (x-r_{2}) (1)

Where:

x - Independent variable.

y - Dependent variable.

a - Vertex constant.

r_{1}, r_{2} - Intercepts of the parabola.

According to the graph, we find that intercepts are 0 and 4, respectively, and a point in the parabola is (x,y) = (3, 2.25). If we know that r_{1} = 0, r_{2} = 4 and (x,y) = (3, 2.25), then the vertex constant is:

a = \frac{y}{(x-r_{1})\cdot (x-r_{2})}

a = -\frac{3}{4}

The equation of the parabola in intercept form is y = -\frac{3}{4}\cdot x\cdot (x-4).

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\bf y=-4x^2-4\implies y=-4x^2+0x-4 \\\\[-0.35em] ~\dotfill\\\\ \textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-4}x^2\stackrel{\stackrel{b}{\downarrow }}{+0}x\stackrel{\stackrel{c}{\downarrow }}{-4} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{0}{2(-4)}~,~-4-\cfrac{0}{4(-4)} \right)\implies (0~,~-4-0)\implies (0,-4)


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