Answered

At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Experience the ease of finding quick and accurate answers to your questions from professionals on our platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

6. Minimum value determined by the formula function f (x) = 2x ²-8x + p was 20. Value f (2) is.
7. Shape factor of the quadratic equation 4x ²-13x = -3 is ...
8. Quadratic function whose graph passes through the point (-12.0) and has a turning point (-15.3) is ..
9. Roots of a quadratic equation: 4x ² + px +25 = 0 are x1 and x2, if the roots of the quadratic equation x1 ² + x2 ² = 12.5 then the value of p is ....
10. Equation x ²-4x +3 = 0 and x ² +4 x-21 = 0, has a root persekutuan.Akar the alliance is 

Sagot :

kate200468
[tex]6)\ \ \ f(x)=2x^2-8x+p\\the\ minimum\ value =20\ \ \ \Leftrightarrow\ \ \ y_{\ of\ vertex}=20\ \ \ \Leftrightarrow\ \ \ - \frac{\Delta}{2a} =20\\\\\Delta=(-8)^2-4\cdot2\cdot p=64-8p\ \ \Leftrightarrow\ \ - \frac{64-8p}{2\cdot2} =20\ \ \Leftrightarrow\ \ -16+2p=20\\\\2p=36\ \ \ \Leftrightarrow\ \ \ p=18\ \ \ \Rightarrow\ \ \ \ f(x)=2x^2-8x+18\\\\f(2)=2\cdot2^2-8\cdot2+18=2\cdot4-16+18=8+2=10[/tex]

[tex]7)\ the\ shape\ factor\ of\ the\ quadratic\ equation\ 4x^2-13x = -3\\ is\ a=4\ \ \ (\ a>0\ \ \ \rightarrow\ \ \ the\ shape\ is\ \cup\ )\\\\8)\ \ \ the\ turning\ point=(-15;3)\ \ \ \Rightarrow\ \ \ f(x)=a(x+15)^2+3\\\\ the\ graph\ passes\ through\ the\ point\ (-12.0) \ \Rightarrow\ \ 0=a(-12+15)^2+3\\\\\Rightarrow\ \ \ a\cdot3^2=-3\ \ \ \Rightarrow\ \ \ a=- \frac{3}{9} =- \frac{1}{3} \ \ \ \Rightarrow\ \ \ f(x)=- \frac{1}{3}(x+15)^2+3[/tex]

[tex] \Rightarrow\ \ \ f(x)=- \frac{1}{3}(x^2+30x+225)+3=- \frac{1}{3}x^2-10x-72\\\\9)\ \ \ 4x^2+px+25=0\\\\\Delta=p^2-4\cdot4\cdot25=p^2-400\\\\two\ solutions\ \ \Leftrightarrow\ \ \Delta>0\ \ \Leftrightarrow\ \ p^2-40>0\ \ \Leftrightarrow\ \ (p-20)(p+20)>0\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \Leftrightarrow\ \ \ p\in(-\infty;\ -20)\ \cap\ (20;\ +\infty)\\-------------------------------[/tex]

[tex]the\ Vieta's\ formulas\ to\ the\ quadratic\ equation\ ax^2+bx+c=0\\\\x_1+x_2=- \frac{b}{a} \ \ \ and\ \ \ x_1\cdot x_2= \frac{c}{a} \\------------------------------\\\\x_1+x_2=- \frac{p}{4} \ \ \ and\ \ \ x_1\cdot x_2= \frac{25}{4} \\\\x_1^2+x_2^2=x_1^2+2\cdot x_1\cdot x_2 +x_2^2-2\cdot x_1\cdot x_2 =(x_1+x_2)^2-2\cdot x_1\cdot x_2 \\\\x_1^2+x_2^2=(x_1+x_2)^2-2\cdot x_1\cdot x_2 \ \ \ \Leftrightarrow\ \ \ 12.5=(- \frac{p}{4} )^2-2\cdot \frac{25}{4} \\\\[/tex]

[tex]12.5= \frac{p^2}{16} +12.5 \ \ \ \Leftrightarrow\ \ \ \frac{p^2}{16}=0 \ \ \ \Leftrightarrow\ \ \ p^2=0 \ \ \ \Leftrightarrow\ \ \ p=0\\\\\\10)\ \ \ x^2-4x+3=0\ \ \ and\ \ \ x^2+4x-21=0\\\\ x^2-4x+3=x^2+4x-21\ \ \Leftrightarrow\ \ -4x-4x=-21-3\\\\\ \ \Leftrightarrow\ \ -8x=-24\ \ \Leftrightarrow\ \ x=3[/tex]
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.