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Compare Y-intercept of Two Quadratic Function

Converting the vertex form to standard quadratic form is useful in determining the difference between the y-intercept between two quadratic functions



REMEMBER :
y - intercept is the value of y when you set x variable to zero ( x = 0)

When x = 0, f(x) = f(0) : meaning substitute all x with value 0 then simplify the answer.
Answer : y-intercept of f(x) = f(0) = 1
Solution: f(0) = (0)² + 4(0) + 1

When x = 0, g(x) = g(0) : meaning substitute all x with value 0 then simplify the answer.
Answer : y-intercept of g(x) = g(0) = 6
Solution: g(0) = -(0)² + 0 + 6

Therefore, the Y-intercept difference between g(x) and f(x) is 6 - 1 = 5

A challenge question is given the vertex and one point of two quadratic equations, solve for the difference of their y-intercept. The problem is the same but you need to apply your knowledge of quadratic standard form and vertex form.

Here you need to solve first for the quadratic equation in standard form for both given quadratic equation. For example quadratic equation g(x) : Given vertex (0.5, 6.25) and one point along its curve (3,0).

g(x) = -x² + x + 6 using given vertex and point. See the blue graph of quadratic equation.

The second quadratic equation f(x) : Given vertex (-2, -3) and one point along its curve (-1, -2)

f(x) = x² + 4x + 1 using given vertex and point. See the red graph of quadratic equation.

Shown below is the combine formula and calculator to speed up your calculation.

Given vertex of a parabola

= ( h , k )

and a point on its curve.
= ( , )

ANSWER
The derive quadratic equation in standard form ( y = ax² + bx + c ) given the vertex point and one point on its curve.

=
a = ² + b = + c =
f(x) = x² + 4x + 1
g(x) = -x² + x + 6
y = ax² + bx + c

f(x) = ax² + bx + c

Solving the value of by using vertex form, y = a(x-h)² + k and substitute the value of its vertex (h = -2, k = -3)
and a point (x = -1 , y = -2).

= ( x - h ) ² + k

+ =

=

Solving the value of = - h * 2a

= - - h * 2 a

=

Solving the value of = k + (b²/4a)

= k + ( ² b ² / 4 a )

=

Parabola (same as Quadratic Equation) Lesson Learned

Vertex Calculator

Equivalent Polynomial Calculator

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