Respuesta :
Answer:
y = 3x² + 21x - 24
Explanation:
A quadratic function can be expressed in the following form:
y = a(x-p)(x-q)
Where p and q are the x-intercepts of the graph. Since the graph passes through the points (-8, 0) and (1, 0), we can say that the x-intercepts are -8 and 1. So, the equation can be written as:
y = a(x - (-8))(x - 1)
y = a( x + 8)( x - 1)
Now, we need to find the value of a, so using the point (2, 30), we can write the following equation:
y = a( x + 8)( x - 1)
30 = a(2 + 8)( 2 - 1)
So, solving for a, we get:
[tex]\begin{gathered} 30=a(10)(1) \\ 30=a\cdot(10) \\ \frac{30}{10}=\frac{a\cdot10}{10} \\ 3=a \end{gathered}[/tex]Therefore, the equation of the quadratic function that passes through the points (-8,0), (1,0), and (2, 30) is:
[tex]y=3(x+8)(x-1)[/tex]Finally, to write the equation in standard form, we need to solve the expression as follows:
[tex]\begin{gathered} y=(3x+3\cdot8)(x-1) \\ y=(3x+24)(x-1) \\ y=(3x\cdot x)-(3x\cdot1)+(24\cdot x)-(24\cdot1) \\ y=3x^2-3x+24x-24 \\ y=3x^2+21x-24 \end{gathered}[/tex]So, the answer is:
y = 3x² + 21x - 24
