Find the x and y Intercepts y=-4x^2+8x-3

$y = - 4 x^{2} + 8 x - 3$

Step 1

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = - 4 x^{2} + 8 x - 3$

Solve the equation.

Rewrite the equation as $- 4 x^{2} + 8 x - 3 = 0$ .

$- 4 x^{2} + 8 x - 3 = 0$

Factor the left side of the equation.

Factor $- 1$ out of $- 4 x^{2} + 8 x - 3$ .

Factor $- 1$ out of $- 4 x^{2}$ .

$- (4 x^{2}) + 8 x - 3 = 0$

Factor $- 1$ out of $8 x$ .

$- (4 x^{2}) - (- 8 x) - 3 = 0$

Rewrite $- 3$ as $- 1 (3)$ .

$- (4 x^{2}) - (- 8 x) - 1 \cdot 3 = 0$

Factor $- 1$ out of $- (4 x^{2}) - (- 8 x)$ .

$- (4 x^{2} - 8 x) - 1 \cdot 3 = 0$

Factor $- 1$ out of $- (4 x^{2} - 8 x) - 1 (3)$ .

$- (4 x^{2} - 8 x + 3) = 0$

Factor.

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 4 \cdot 3 = 12$ and whose sum is $b = - 8$ .

Factor $- 8$ out of $- 8 x$ .

$- (4 x^{2} - 8 x + 3) = 0$

Rewrite $- 8$ as $- 2$ plus $- 6$

$- (4 x^{2} + (- 2 - 6) x + 3) = 0$

Apply the distributive property.

$- (4 x^{2} - 2 x - 6 x + 3) = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$- ((4 x^{2} - 2 x) - 6 x + 3) = 0$

Factor out the greatest common factor (GCF) from each group.

$- (2 x (2 x - 1) - 3 (2 x - 1)) = 0$

Factor the polynomial by factoring out the greatest common factor, $2 x - 1$ .

$- ((2 x - 1) (2 x - 3)) = 0$

Remove unnecessary parentheses.

$- (2 x - 1) (2 x - 3) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$2 x - 1 = 0$

$2 x - 3 = 0$

Set $2 x - 1$ equal to $0$ and solve for $x$ .

Set $2 x - 1$ equal to $0$ .

$2 x - 1 = 0$

Solve $2 x - 1 = 0$ for $x$ .

Add $1$ to both sides of the equation.

$2 x = 1$

Divide each term in $2 x = 1$ by $2$ and simplify.

Divide each term in $2 x = 1$ by $2$ .

$\frac{2 x}{2} = \frac{1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{1}{2}$

Divide $x$ by $1$ .

$x = \frac{1}{2}$

Set $2 x - 3$ equal to $0$ and solve for $x$ .

Set $2 x - 3$ equal to $0$ .

$2 x - 3 = 0$

Solve $2 x - 3 = 0$ for $x$ .

Add $3$ to both sides of the equation.

$2 x = 3$

Divide each term in $2 x = 3$ by $2$ and simplify.

Divide each term in $2 x = 3$ by $2$ .

$\frac{2 x}{2} = \frac{3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{3}{2}$

Divide $x$ by $1$ .

$x = \frac{3}{2}$

The final solution is all the values that make $- (2 x - 1) (2 x - 3) = 0$ true.

$x = \frac{1}{2}, \frac{3}{2}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{1}{2}, 0), (\frac{3}{2}, 0)$

Step 2

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = - 4 {(0)}^{2} + 8 (0) - 3$

Solve the equation.

Remove parentheses.

$y = - 4 \cdot 0^{2} + 8 (0) - 3$

Remove parentheses.

$y = - 4 {(0)}^{2} + 8 (0) - 3$

Simplify $- 4 {(0)}^{2} + 8 (0) - 3$ .

Simplify each term.

Raising $0$ to any positive power yields $0$ .

$y = - 4 \cdot 0 + 8 (0) - 3$

Multiply $- 4$ by $0$ .

$y = 0 + 8 (0) - 3$

Multiply $8$ by $0$ .

$y = 0 + 0 - 3$

Simplify by adding and subtracting.

Add $0$ and $0$ .

$y = 0 - 3$

Subtract $3$ from $0$ .

$y = - 3$

y-intercept(s) in point form.

y-intercept(s): $(0, - 3)$

Step 3

List the intersections.

x-intercept(s): $(\frac{1}{2}, 0), (\frac{3}{2}, 0)$

y-intercept(s): $(0, - 3)$

Step 4

Find the x and y Intercepts y=-4x^2+8x-3

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