Q. \(x^2+3x-4\)

Q: Solve x^2+3x-4=0?

Using (x+4)(x-1)=0, roots are x=-4 and x=1.

Q: Find the roots using the quadratic formula?

For a=1,b=3,c=-4: x=\frac{-3\pm\sqrt{9+16}}{2}=\frac{-3\pm5}{2}, so x=1,-4.

Q: What is the discriminant of x^2+3x-4?

\Delta=b^2-4ac=3^2-4(1)(-4)=9+16=25.

Q: What is the vertex of the parabola y=x^2+3x-4?

x_v=-\frac{b}{2a}=-\frac{3}{2}. Then y_v=\left(-\frac{3}{2}\right)^2+3\left(-\frac{3}{2}\right)-4=-\frac{25}{4}.

Q: What is the y-intercept of x^2+3x-4?

Set x=0. Then y=-4, so the intercept is (0,-4).

Q: What are the x-intercepts of x^2+3x-4?

Set y=0. From (x+4)(x-1)=0, intercepts are (-4,0) and (1,0).

Answer

We factor the quadratic.

\[
x^2+3x-4=(x+4)(x-1)
\]

Set each factor to zero:

\[
x+4=0 \Rightarrow x=-4,\quad x-1=0 \Rightarrow x=1
\]

Final result: The factorization is \( (x+4)(x-1) \), and the solutions are \( x=-4 \) and \( x=1 \).

Detailed Explanation

We want to work with the expression

\(x^2 + 3x – 4\).

Step 1: Factor the quadratic.

To factor \(x^2 + 3x – 4\), we look for two numbers that:

1. Multiply to \(x^2 \cdot (-4) = -4\).

2. Add to \(3\).

The factors of \(-4\) are \(1\cdot (-4)\) and \((-1)\cdot 4\). Now check which pair adds to \(3\):

\(-1 + 4 = 3\).

So the quadratic factors as:

\[
x^2 + 3x – 4 = (x – 1)(x + 4).
\]

Final Answer:

\[
\boxed{x^2 + 3x – 4 = (x – 1)(x + 4)}
\]

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Algebra FAQ

Factor \(x^2+3x-4\)?

\(x^2+3x-4=(x+4)(x-1)\).

Solve \(x^2+3x-4=0\)?

Using \((x+4)(x-1)=0\), roots are \(x=-4\) and \(x=1\).

Find the roots using the quadratic formula?

For \(a=1,b=3,c=-4\): \(x=\frac{-3\pm\sqrt{9+16}}{2}=\frac{-3\pm5}{2}\), so \(x=1,-4\).

What is the discriminant of \(x^2+3x-4\)?

\(\Delta=b^2-4ac=3^2-4(1)(-4)=9+16=25\).

What is the vertex of the parabola \(y=x^2+3x-4\)?

\(x_v=-\frac{b}{2a}=-\frac{3}{2}\). Then \(y_v=\left(-\frac{3}{2}\right)^2+3\left(-\frac{3}{2}\right)-4=-\frac{25}{4}\).

What is the \(y\)-intercept of \(x^2+3x-4\)?

Set \(x=0\). Then \(y=-4\), so the intercept is \((0,-4)\).

What are the \(x\)-intercepts of \(x^2+3x-4\)?

Set \(y=0\). From \((x+4)(x-1)=0\), intercepts are \((-4,0)\) and \((1,0)\).

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