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How do you write the equation of the parabola in vertex form given vertex (-3,4); x-intercept -1?

Answer 1

#y=-(x+3)^2+4#

The equation of a parabola in #color(blue)"vertex form"# is.

#color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))# where (h , k) are the coordinates of the vertex and a is a constant.

#"here " (h,k)=(-3,4)#

#rArry=a(x+3)^2+4#

#"x-intercept is -1 "rArr(-1,0)" is a point on the parabola"#

#"using " (-1,0)" to find a"#

#0=a(-1+3)^2+4#

#rArr4a+4=0rArra=-1#

#rArry=-(x+3)^2+4larrcolor(red)" equation in vertex form"# graph{-(x+3)^2+4 [-10, 10, -5, 5]}

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Answer 2

Jameson Allen

The equation of the parabola in vertex form is ( y = a(x - h)^2 + k ), where ( (h, k) ) is the vertex. Given the vertex ((-3, 4)), we have ( h = -3 ) and ( k = 4 ). To find ( a ), substitute the x-intercept (-1) into the equation. So, ( 0 = a(-1 - (-3))^2 + 4 ). Solving for ( a ), ( a = \frac{4}{4} = 1 ). Therefore, the equation of the parabola in vertex form is ( y = (x + 3)^2 + 4 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.